Targeted communication is made possible using beamforming. It is extensively employed in many disciplines involving electromagnetic waves, including arrayed ultrasonic, optical, and high-speed wireless communication. Conventional beam steering often requires the addition of separate active amplitude and phase control units after each radiating element. The high-power consumption and complexity of large-scale phased arrays can be overcome by reducing the number of active controllers, pushing beamforming into satellite communications and deep space exploration. To address this, we propose a phased array antenna design based on dimensionality-reduced cascaded angle offset phased array (DRCAO-PAA). By applying singular value decomposition (SVD) to compress the coefficient matrix of phase shifts, our method reduces the number of active controllers while maintaining beam-steering performance. Furthermore, the suggested DRCAO-PAA was sing the singular value deposition concept. For practical application the particle swarm optimization algorithm and deep neural network Transformer were adopted. Based on this theoretical framework, an experimental board was built to verify the theory. Finally, the 16/8/4 -array beam steering was demonstrated by using 4/3/2 active controllers, respectively.

Latent factor models are valuable in bioinformatics for accounting for unmeasured variation alongside observed covariates. Yet many methods struggle to separate known effects from latent structure and to handle losses beyond standard regression. We present a unified framework that augments row and column predictors with a low-rank latent component, jointly modeling measured effects and residual variation. To remove ambiguity in estimating observed and latent effects, we impose a carefully designed set of orthogonality constraints on the coefficient and latent factor matrices, relative to the spans of the predictor matrices. These constraints ensure identifiability, yield a decomposition in which the latent term captures only variation unexplained by the covariates, and improve interpretability. An efficient algorithm handles general non-quadratic losses via surrogates with monotone descent. Each iteration updates the latent term by truncated singular value decomposition of a doubly projected residual and refines coefficients by projections. The number of latent factors is selected by applying an elbow rule to a degrees-of-freedom-adjusted information criterion. A parametric bootstrap provides valid inference on feature-outcome associations under the regularized low-rank structure. Applied to real pharmacogenomic data, the method recovers biologically coherent gene-drug associations missed by standard factor models, such as the EGFR-inhibitor link, highlights novel candidates with plausible mechanisms, and reveals gene programs aligned with compound modes of action, including a latent unfolded-protein-response module affecting drug sensitivity. These results support the framework’s utility for precision oncology, yielding stronger biomarkers for patient stratification and deeper insight into drug resistance mechanisms.

The liquid crystalline 11OS5 compound, forming the nematic phase and a few smectic phases, is investigated by broadband dielectric spectroscopy and infrared spectroscopy. The dielectric relaxation times, ionic conductivity, and positions of infrared absorption bands corresponding to selected intramolecular vibrations are determined as a function of temperature in the range from an isotropic liquid to a crystal phase. The correlation coefficient matrix and k-means cluster analysis of infrared spectra are tested for detection of phase transitions. The density-functional theory calculations are carried out for interpretation of experimental infrared spectra. The performance of various basis sets and exchange-correlation functionals is compared, including both agreement of scaled calculated band positions with experimental values and computational time. The intermolecular interactions in the crystal phase are inferred from the experimental IR spectra and density-functional theory calculations for dimers in head-to-head and head-to-tail configurations. The experimental temperature dependence of the C═O stretching band suggests that the head-to-tail configuration in the crystal phase is more likely. A significant slowing down of the flip-flop relaxation process is observed at the transition between the smectic C and hexagonal smectic X phases.

Purpose: Reinforcement Learning (RL) is attracting great interest because it enables systems to learn by interacting with the environment. This study aims to enhance the RL algorithm to become more similar to human motor control by combining it with the Non-negative matrix factorization (NMF) method. Materials and Methods: In the study, the signals recorded from six muscles involved in arm-reaching movement without carryinga certain weight.were pre-processed, and the optimal number of synergy patterns was extracted using NMF and the Variance Account For (VAF) methods. This, in turn, contributes to reducing the calculations. Subsequently, the robustness of the two-link arm model with six muscles was evaluated under various noise levels applied to the action coefficient matrix. Finally, the average synergy pattern was done on the mentioned arm model, and the RL algorithm controlled it by producing the action coefficient matrix. Results: The average VAF% was 97.25±0.45%, and the number of synergies was four. The tip-of-the-arm model was able to reach the target after an average of 100 episodes. Conclusion: The results indicated that the similarity in the extracted synergy patterns helps to model a system that is more similar to motor control. Additionally, the results of the synergistic patterns revealed that the two-link arm model with six muscles was suitable for the model. While controlling the model with the RL algorithm, the desired end-point position and path were achieved.

We establish that frame flows for geometrically finite hyperbolic manifolds of arbitrary dimensions \Gamma \backslash \mathbb{H}^{d+1} are exponentially mixing with respect to the Bowen–Margulis–Sullivan measure, which is the measure of maximal entropy. This paper focuses on the remaining case, the case with cusps . To prove this, we utilize the countably infinite symbolic coding and perform a frame flow version of Dolgopyat’s method à la Sarkar–Winter and Tsujii–Zhang. This requires the local non-integrability condition and the non-concentration property but the challenge in the presence of cusps is that the latter holds only on a large proper subset. To overcome this, we use an effective renewal theorem to prove a uniform large deviation property for symbolic recurrence to the large subset, inspired by the work of Li. Applications of the main theorem include an asymptotic formula for matrix coefficients for L^{2}(\Gamma \backslash \mathrm{SO}(d+1, 1)^{\circ}) with an exponential error term, and exponential equidistribution of holonomies and translates of horospherical orbits.

This paper studies a quantum simulation technique for solving the Fokker-Planck equation. Traditional semi-discretization methods often fail to preserve the underlying Hamiltonian dynamics and may even modify the Hamiltonian structure, particularly when incorporating boundary conditions. We address this challenge by employing the Schrödingerization method – it converts any linear partial and ordinary differential equation with non-Hermitian dynamics into systems of Schrödinger-type equations. It does so via the so-called warped phase transformation that maps the equation into one higher dimension. We explore the application in two distinct forms of the Fokker-Planck equation. For the conservation form, we show that the semidiscretization-based Schrödingerization is preferable, especially when dealing with non-periodic boundary conditions. Additionally, we analyze the Schrödingerization approach for unstable systems that possess positive eigenvalues in the real part of the coefficient matrix or differential operator. Our analysis reveals that the direct use of Schrödingerization has the same effect as a stabilization procedure. For the heat equation form, we propose a quantum simulation procedure based on the time-splitting technique, and give explicitly its corresponding quantum circuit. We discuss the relationship between operator splitting in the Schrödingerization method and its application directly to the original problem, illustrating how the Schrödingerization method accurately reproduces the time-splitting solutions at each step. Furthermore, we explore finite difference discretizations of the heat equation form using shift operators. Utilizing Fourier bases, we diagonalize the shift operators, enabling efficient simulation in the frequency space. Providing additional guidance on implementing the diagonal unitary operators, we conduct a comparative analysis between diagonalizations in the Bell and the Fourier bases, and show that the former generally exhibits greater efficiency than the latter.

Self-consistent-field (SCF) in the grand-canonical (GC) ensemble faces convergence difficulties with significant fractional occupation at low temperatures. By recognizing the orbital coefficient matrix and the fractional occupation vectors as two independent variables, this work provides a new viewpoint upon GC-SCF as an optimization problem on a product manifold of a flag manifold and a Euclidean space. During the optimization process, the manifold is automatically adjusted to the orbitals, which are divided into three partitions based on the occupation numbers, so that the occupation numbers are optimized properly, avoiding notorious gradient explosion and vanishing. Important concepts in manifold optimization are discussed and their specific expressions in GC-SCF are given. Via numerical benchmarks on various examples, our algorithms are shown to be more efficient than the conventional direct inversion in the iterative subspace (DIIS). Among them, we recommend the augmented Roothaan-Hall method, which reaches the balance between time consumption and convergence rate.

In this paper, we propose two low-complexity multiple-input multiple-output (MIMO) equalization schemes for short-reach coherent-lite optical interconnects: dynamic pruning MIMO (DP-MIMO) and dynamic clustering MIMO (DC-MIMO). Based on the conventional 4 × 4 real-valued (RV) MIMO architecture, both schemes aim to reduce the computational complexity of each channel filter according to real-time channel characteristics. DP-MIMO sparsifies filter coefficient matrices and dynamically adjusts the sparsity level of each channel filter based on the energy distribution across all channels, achieving adaptive tap optimization. DC-MIMO reduces redundant computations by clustering filter coefficients and further introduces an energy-adaptive mechanism that dynamically adjusts the number of clusters, balancing complexity and system performance. To further evaluate the benefits of the energy-adaptive mechanism, the static pruning MIMO (SP-MIMO) and static clustering MIMO (SC-MIMO) are also introduced as their static counterparts. The proposed schemes are experimentally validated in a C-band 80-GBaud dual-polarization 16QAM (DP-16QAM) system over 1-km, 2-km, and 5-km standard single-mode fiber (SSMF) links. Experimental results show that, compared with conventional 4 × 4 RV MIMO, DP-MIMO can achieve around 40% reduction in real-valued multiplications (RMs) per transmitted symbol within a 0.20-dB receiver optical power (ROP) penalty. Compared with SP-MIMO at a similar complexity level, DP-MIMO introduces a smaller ROP penalty. DC-MIMO achieves around 60% RMs reduction within a 0.15-dB ROP penalty compared with 4 × 4 RV MIMO, and compared with SC-MIMO at similar performance, DC-MIMO achieves lower complexity. To verify the robustness of the proposed schemes against in-phase/quadrature (IQ) skew impairments, an additional 2-ps IQ skew was introduced. Both DP-MIMO and DC-MIMO maintain stable performance under this condition, with DP-MIMO reducing around 40% of complexity within a 0.2-dB ROP penalty and DC-MIMO reducing around 60% of complexity within a 0.1-dB ROP penalty.

The study of \(D\)-stability in mathematical analysis is crucial for understanding and ensuring the stability of linear dynamical systems. This article introduces novel findings on the characterization of \(D\)-stability, along with its connections to additive \(D\)-stability concerning speed and coordinate transformations in linear dynamical systems with \(n\) degrees of freedom\[A \frac{d^2\mu(\tau)}{d\tau^2} + B \frac{d\mu(\tau)}{d\tau} + C \mu(\tau) = 0, \ \tau \in \mathbb{R}, \ \tau > 0,\]Consider the stiffness, mass, and damping matrices \(A, B, C \in \mathcal{M}^{n \times n}\), and let \( \mu(\tau) \in \mathbb{R}^n \) denote the vector of generalized coordinates with \(\frac{d\mu(\tau)}{d\tau}\) representing its corresponding velocity vector. This work derives new theoretical insights into \(D\)-stability, additive \(D\)-stability with respect to velocity, and additive \(D\)-stability concerning coordinate transformations. These results are established using techniques from linear algebra, matrix theory, dynamical systems, and their connections to structured singular value computations. Additionally, numerical investigations of the spectrum, singular values, and pseudospectra of the coefficient matrices \(A, B, C \in \mathcal{M}^{n \times n}\) are conducted using EigTool, providing further validation of the theoretical framework.

Addressing uncertainties on the demand side caused by electricity price fluctuations during integrated energy system (IES) dispatch, modeling biases resulting from static assumptions about equipment energy efficiency, and cost redundancy issues stemming from unreasonable seasonal allocation of carbon quotas, this study constructs an electricity PDR economic dispatch optimization model incorporating dynamic energy efficiency and dynamic carbon trading. It proposes a “distributed robust optimization (DRO)-model predictive control (MPC)” collaborative framework and a tiered dynamic carbon quota allocation strategy accounting for seasonal output and efficiency variations of equipment, tailored to match carbon emission characteristics across different seasons. At the demand response level, an electricity price elasticity coefficient matrix is introduced to quantify the impact of real-time price fluctuations on load, integrating it into the MPC model to resolve the time-scale mismatch between day-ahead and intraday scheduling. Simulation results demonstrate: The coupled dynamic energy efficiency and carbon trading model reduces total system costs by 13.07% and carbon trading costs by 11.57% compared to the conventional approach. Regarding tracking error, the combination of rolling optimization and feedback correction improves tracking accuracy by 14.66% and 6.13% compared to cases without feedback correction and rolling optimization, respectively, while reducing total costs by 4.36% compared to the case without rolling optimization. This study provides a scientifically feasible optimization solution for low-carbon economic dispatch of IES under uncertainty.

ABSTRACT The Multi-Dimensional Small Baseline Subset Interferometric Synthetic Aperture Radar (MSBAS InSAR) technique significantly reduces the visual ambiguity caused by the single line of sight by integrating multi-orbit SAR data for joint solution. However, due to temporal-spatial decorrelation, topographic errors, orbital errors and phase unwrapping, different orbit data usually have different error statistical characteristics, and it is unreasonable to set the equal weight for ascending and descending observations in the inversion process of the existing MSBAS InSAR deformation model. In addition, the close acquisition times of ascending and descending data lead to strong multicollinearity among the column vectors of the design matrix, and the coefficient matrix of the non-regularized MSBAS solution exhibits a severe ill-posedness, with a condition number on the order of 1018, which makes the solution extremely sensitive to noise and results in unstable weight estimation. Hence, MSBAS InSAR deformation modelling method based on regularized variance component estimation (MSBAS-RVCE) is proposed, in which the regularization method is used to ensure stable model solutions, while iterative refinement of the weight matrix provides accurate posterior variances and enhances result reliability. The proposed method was applied to MSBAS InSAR deformation monitoring in the Jiyang mining area. Comparative analysis of subsidence values, profiles, levelling data and InSAR results demonstrates that the proposed method reasonably determines the weight ratio of ascending and descending data in the joint adjustment and improves the accuracy of the results by approximately 35% compared with the equal-weight strategy.

This paper investigates the adaptive event-triggered stabilisation for a class of uncertain parabolic PDE-ODE systems. Remarkably, different from the related literature where uncertainties are severely constrained, more serious uncertainties are involved since both the system matrices in ODE subsystems are linearly parameterised by unknown constants while the diffusion coefficient and the reaction coefficient matrix in PDE subsystems are unknown. Such an ingredient leads to the incapability of the traditional methods. For this, a novel control strategy is proposed by a skilful combination of infinite-dimensional backstepping method, adaptive technique with the constructive method for dynamic event-triggered mechanism. Specifically, a couple of infinite-dimensional backstepping transformations are first introduced to change the original system into a new one. For the new system, an adaptive controller is explicitly designed joint with an event-triggered mechanism in which the updating law of a pivotal dynamic threshold is smartly chosen. Then, much effort has to be taken to show its stability, i.e. all the states of the resulting closed-loop system is bounded while the original system states converge to zero along with the avoidance of the infinitely fast sampling/execution. Finally, an example is given to validate the effectiveness of the proposed results.

Multi-view subspace clustering (MSC) has received widespread attention due to its ability to efficiently exploit consensus and diversity information from multiple perspectives. However, existing methods focus more on inter-view diversity and ignore the consistent associations and higher-order features among views under different perspectives. To solve the above problems, an auto-weighted MSC with consistency learning (AWMSCC) is proposed. Specifically, this method first integrates the shared features of all coefficient matrices in a three-factor decomposition to construct a new shared consistency matrix. Then, by using the tensor low-rank constraint, the coefficient matrices and the shared consistency matrix are stacked into a third-order tensor to achieve effective propagation of inter-view consistency information. Finally, the appropriate weights are adaptively assigned to all matrix information to obtain a high-quality affinity matrix. Experimental results on four benchmark datasets show that AWMSCC outperforms seven other advanced clustering algorithms in terms of performance.

This study develops and tests a MATLAB program for neutralising systems with upper triangular coefficient matrices. Augmented matrices for systems of linear equations are reduced to produce a neutral (identity matrix) left hand side, at which point the right hand side has the solutions for the system. A strategy for minimal error is pursued, where elimination operations must be completed in one step for each number. The strategy was expressed in pseudocode, a flowchart developed, and then the program was coded in MATLAB. The program was tested for four sample augmented matrices of varying sizes. The results demonstrated that the program was 100% accurate. The technique can be applied to any square matrix system, since any square matrix can be expressed as an upper triangular matrix. The automation of matrix operations and achievement of 100% accuracy allows for the use of the program for very large data sets, extending the potential for research with accurate finding.

Based on the input-output analysis theory from the perspective of organizational economics, this study utilizes direct consumption coefficient matrices, total consumption coefficient matrices, and the Leontief inverse matrix to analyze the economic linkages among the textile finished products, pharmaceutical products, and health sectors. The results indicate that the pharmaceutical products sector exhibits significant "core-driven" and self-reinforcing characteristics, forming a deeply symbiotic relationship with the health sector. In contrast, the textile finished products sector demonstrates a "marginal supporting" role with relatively weak linkages. The study proposes that promoting the transformation of the textile sector into high-value-added fields such as medical textiles can foster synergistic development among the three sectors, providing a basis for optimizing industrial policies and enhancing supply chain resilience.

Based on a decoupling assumption made for approximating the wheelset responses, this paper presents a physically meaningful wheel-rail force model along with an efficient decoupled method for random vibration analysis of the train-bridge interaction problems. Specifically, the wheel-rail forces are treated as a multi-variate stationary random process statistically characterized by its spectral density matrix, obtained through stochastic analysis of the train equation incorporating only the track irregularity while excluding the train gravity. Next, the obtained spectral density matrix is decomposed through the spectral representation technique, yielding a discrete formulation of the wheel-rail forces with respects to a pair of orthogonal stochastic vectors (OSVs). Then, the Duhamel integral is employed to derive explicit relations between the bridge response and the OSVs, with the associated coefficient matrices efficiently determined using a recursive scheme derived based on the Newmark integration algorithm. The resulting response-OSVs expression allows for statistical calculation of the bridge responses in a decoupled manner, avoiding iterative computations or repeated system matrix updates typically required in coupled stochastic analyses of train-bridge systems. Lastly, the proposed method is numerically demonstrated through stochastic analysis of a three-span continuous bridge subjected to train loads, with comparisons made to the Monte Carlo simulation, pseudo-excitation method and a fully coupled approach. The numerical results suggest that, compared with traditional coupled approach, the proposed decoupled strategy improves significantly the computational efficiency, particularly for cases involving a large number of vehicles.

ABSTRACT Eigenvalue and eigenvector sensitivities with respect to design parameters are crucial for advancing design, optimization, and uncertainty quantification in structural systems. This paper introduces a novel, efficient, and general numerical method for computing arbitrary‐order sensitivities of eigenpairs in self‐adjoint undamped and underdamped systems. The proposed approach integrates Hypercomplex Automatic Differentiation (HYPAD) with a residual‐based formulation to compute sensitivities with machine precision. Sensitivities are calculated in ascending order by solving a sequence of linear systems that share a common coefficient matrix. The method preserves the sparsity of the mass and stiffness matrices, allowing for efficient factorization and compatibility with current sparse direct solvers. The methodology is demonstrated through a numerical example under both undamped and underdamped conditions. Up to tenth‐order sensitivities are computed with respect to multiple material and geometric parameters, showing excellent agreement with analytical solutions. Runtime analysis confirms that the computational cost per derivative remains constant, regardless of the order, underscoring the method's efficiency. Overall, the proposed approach offers a scalable and accurate framework for sensitivity analysis in large‐scale eigenvalue problems.

ABSTRACT This article considers modelling large-dimensional matrix time series by introducing a regression term to the existing matrix factor model. This is an indispensable addition, since in practice there always exist some known factors which are among the driving forces. Asymptotic properties are established to ensure the consistency of our procedure for estimating the coefficient matrix, the loading matrices and the signal part. To verify the suitability of our estimation procedure, we carry out a set of simulation studies with finite samples. Finally, empirical studies on daily returns of multi-national stocks demonstrate the superiority of the proposed model.

This paper presents a wavelet-based numerical method for solving time–space fractional advection equations involving Caputo derivatives. The governing equation is given by \[d_1 \frac{\partial^{\beta} W}{\partial z^{\beta}} + d_2 \frac{\partial^{\gamma} W}{\partial u^{\gamma}} = h(z, u),\]where \( 0 < \beta, \gamma \leq 1 \) denote the fractional orders in the Caputo sense, and \( h(z,u) \) is a known source function. The proposed scheme uses a collocation approach based on Euler wavelets—compactly supported bases constructed from shifted and scaled Euler polynomials. This structure enables exact symbolic evaluation of fractional derivatives and facilitates the accurate enforcement of boundary conditions. The numerical framework builds the solution through coefficient matrices and vector terms derived from a symbolic system, ensuring consistency with the governing equation at carefully selected collocation points. A central result shows that, when the exact solution is polynomial and symbolic computation is used, the method reproduces the solution exactly at all collocation nodes.Numerical experiments support the theoretical findings, demonstrating high accuracy and computational efficiency, particularly for smooth solutions where rapid convergence is observed. Compared to existing approaches, the method offers enhanced precision and broader applicability, especially for problems involving coupled space–time nonlocality. This work expands the use of Euler wavelets in the context of fractional partial differential equations and provides a mathematically rigorous framework suitable for future extensions to nonlinear and multidimensional problems.

Tensorized multi-dimensional multi-view clustering based on nonnegative matrix factorization.