Search Results (121)

The severe susceptibility of qubits to environmental noise remains the primary obstacle to practical quantum computing. To overcome this, we introduce a purification-assisted quantum error-correction (QEC) framework that embeds a symmetric subspace projection module between the encoding and physical layers. Acting as an information-theoretic noise-entropy filter, it compresses von Neumann entropy before encoding. Under depolarizing noise, a three-copy scheme elevates the surface-code threshold from 1.1% to a 2.0% noiseless bound (~1.6% at circuit level). Our iterative purification-assisted error-correction (IPEC) algorithm dynamically modulates purification depth via syndrome feedback, delivering a 46-fold logical error reduction for surface codes (d = 7) at a 1.0% physical error rate. Full article

Accurate Unmanned Aerial Vehicle (UAV) position estimation is the cornerstone of urban low-altitude safety management systems. Time Difference of Arrival (TDOA) and Remote Identification (Remote ID) are widely used surveillance technologies with complementary characteristics. TDOA provides high-rate updates but suffers from geometry-induced horizontal–vertical anisotropy and multipath effects, while Remote ID supplies absolute state information yet struggles with intermittent sampling and packet loss. Existing fusion schemes typically address these issues in isolation: sequential filtering manages asynchrony but assumes Gaussian noise, robust estimators suppress outliers at the cost of discarding valid data, and coupled-filter architectures allow vertical anomalies to contaminate horizontal estimates through the Kalman gain cross-coupling. No prior framework jointly handles structural TDOA altitude jumps, stochastic Remote ID timing jitter, and the geometric anisotropy between estimation subspaces within a single coherent pipeline. To bridge this gap, we propose a Hybrid Conditional Kalman Filter (HCKF) framework comprising three integrated modules. First, a kinematics-based temporal alignment module maps asynchronous measurements onto a uniform timeline and predicts missing samples, resolving cross-modal time mismatches. Second, a measurement quality evaluation mechanism detects TDOA altitude steps via robust two-layer stratification and scores Remote ID timing irregularity through a confidence mapping, converting these anomalies into dynamic covariance adjustments and weight caps without discarding observations. Third, a Subspace-Decoupled Fusion strategy exploits the physical insight that TDOA horizontal precision derives from hyperbolic intersection geometry, whereas its vertical estimates suffer from weak observability due to near-coplanar ground-station deployment. By applying entropy-guided weighting in the horizontal plane and a conditional Remote ID-dominant rule in the vertical axis, this design prevents cross-dimensional error propagation. The framework was validated using three real-world flight missions at distinct altitudes (255 m, 345 m, and 440 m) totaling 13.51 km of flight distance, with RTK serving as ground truth. HCKF reduces the Root Mean Square Error by over 40% relative to single-source baselines (95% bootstrap confidence interval: [35.2%, 48.7%]), and paired Wilcoxon signed-rank tests confirm statistically significant improvement ($p<0.01$) over standard EKF, Covariance Intersection, and Iterative CI across all three tracks. Full article

This article reviews the linear solvers available in OpenFOAM and assesses their impact on the convergence behaviour of the SIMPLE algorithm. The discretisation of transport equations in CFD results in large and sparse linear systems, for which the choice of linear solver strongly influences the computational time. Although the solver does not change the final discrete solution, the difference in speed and robustness between the solvers can be more than one order of magnitude. A brief overview is given concerning how the velocity and pressure fields are decoupled in OpenFOAM, followed by a detailed review of the main linear solver families, including direct methods, basic iterative methods, multigrid methods and Krylov subspace methods, with attention to their practical strengths and weaknesses. The performance of the most advanced solvers is evaluated on a full-scale non-reacting kiln case consisting of 2.3 million cells. The pressure-corrector equation is identified as the main bottleneck in the SIMPLE algorithm. The conjugate gradient (CG) solver with a multigrid (MG) preconditioner is found to be the fastest and most stable method, achieving speed-ups of up to a factor of 7 compared to the slower advanced methods. Using MG as a preconditioner also improves the robustness of the Bi-CGStab method. Full article

This paper is concerned with the numerical solution of the variable-order time fractional advection–diffusion–reaction equation (VO-TFADRE) in two space dimensions. We first propose a Crank–Nicolson (C-N) discretization scheme based on central difference operators and L1 formula for space and time variables, respectively. Then, we apply the C-N scheme to construct a new algorithm, namely the explicit group (EG) method, for the model problem under consideration. The EG method utilizes the idea of small fixed-size groups of mesh points and comes with computational merits as compared with the C-N scheme. Stability and convergence analyses are given in this work. The resulting discretization leads to large sparse linear systems, which are solved using the Bi-CGSTAB iterative method. Numerical experiments demonstrate that both the C–N and EG schemes achieve accurate approximations, while the EG method significantly reduces computational time. To economize further on the computational cost, we propose a parallelized version of the EG method for solving the VO-TFADRE. Carried out numerical simulations reveal that the parallel algorithm is more efficient than the serial algorithm for solving the problem under consideration. Full article

GPS-based passive bistatic radar (PBR) benefits from global satellite coverage for target surveillance. However, multiple GPS satellites within the PBR mainlobe generate cross-correlation interference (CCI) that severely masks target echoes, reducing the detection probability to zero across significant portions of the surveillance area. Existing reconstruction-based suppression methods rely on iterative frequency estimation, which introduces substantial errors during the convergence stage of the tracking loop, leading to degraded interference suppression performance. This paper proposes an autoregressive steady-state compensation (ARSSC) method to address this limitation. First, a precise carrier frequency estimation model is established to accelerate convergence and improve tracking accuracy. Second, the frequency estimation outputs are partitioned into convergence and steady-state stages, and a p-th order autoregressive (AR) model is fitted to the steady-state estimates. A compensation function is then derived from the AR model to correct the frequency errors in the convergence stage. Finally, the compensated reconstructed CCI signals are used to construct an interference subspace, and a projection-based algorithm suppresses the CCI from the surveillance signal. Simulation results demonstrate that the proposed ARSSC method achieves a maximum interference suppression improvement of 7.4 dB compared to conventional reconstruction approaches. Real-data experiments conducted under different field scenarios further validate the method, yielding a 6.3 dB interference suppression ratio (ISR) improvement over traditional reconstruction techniques in both tested cases. Full article

This paper presents a reinforcement learning (RL) framework based on the Koopman operator for high-dimensional nonlinear control. By leveraging nonlinear eigenvalue dynamics, the approach enables scalable and efficient policy optimization. We examined the challenge of controlling complex systems by embedding high-dimensional states $x\left(t\right)\in {\mathbb{R}}^n$ into a Koopman-invariant subspace $\varphi \left(x\right)\in {\mathbb{R}}^m$, where evolution becomes linear under the Koopman operator $\mathcal{K}$. By spectrally decomposing $\mathcal{K}=U\Lambda U^{-1}$, the eigenvalue dynamics are obtained, and $\mathcal{K}$ is reconstructed iteratively via dominant eigenpairs $\left(v_i,w_i\right)$. A policy network $\pi \left(a|s\right)$ selects actions $u\left(t\right)$, while a value function $V\left(s\right)$, expressed in Koopman eigenfunction coordinates, guides gradient-based policy updates. The framework integrates spectral stability constraints ($\rho \left(X\right)<1)$ and Lyapunov-based analysis to ensure convergence. We derive perturbation bounds for Koopman eigenvalues under policy updates and establish conditions for nonlinear mode interactions in the lifted space. The spectral policy gradient theorem for Koopman RL links eigenvalue dynamics to policy optimization, includes a constrained Bellman formulation in Koopman coordinates, and analyzes bifurcation of learning-induced eigenvalue shifts. Full article

We propose a novel subspace derivative-free conjugate gradient method for solving large-scale nonlinear monotone equations with convex constraints. At each iteration, the search direction is constructed by minimizing a quadratic model within a subspace spanned by the current negative function value vector and the two most recent search directions. The algorithm incorporates a hyperplane projection technique to generate feasible iterative points. Under reasonable assumptions, we establish the global convergence and R-linear convergence rate of the proposed method. Extensive numerical experiments on benchmark problems demonstrate that the new algorithm significantly outperforms state-of-the-art derivative-free methods in terms of number of iterations, function evaluations, and CPU time. The results confirm the efficiency and robustness of the proposed approach for solving large-scale monotone systems. Full article

This article addresses the fault detection (FD) problem for traction drive systems in the presence of unknown noise covariances. The dynamic behavior of the traction drive system, affected by actuator and sensor faults, is first formulated. Following the philosophy of the subspace identification, the system matrices are identified directly from collected process data using QR decomposition and singular value decomposition. Based on the identified model, a robust Kalman filter (KF)-based FD scheme is developed. By exploiting the iterative interaction between the estimator and measurement data within the KF framework, the noise covariance matrices are adaptively estimated, which alleviates the adverse effects caused by empirical covariance selection in conventional KF-based FD methods. Experimental results obtained from a real traction drive system verify the effectiveness and reliability of the proposed approach. Full article

Individual differences and long calibration time present significant challenges to the practical implementation of brain–computer interfaces (BCIs). Domain adaptation technology can help mitigate these challenges by leveraging knowledge from existing subjects. Although domain adaptation methods have achieved progress in BCIs, there remains a need for further exploration in class structure and cross-domain dispersion. In this paper, we propose a novel framework, multi-constrained transfer learning with selective pseudo-label update (MCTLP). First, Euclidean alignment is applied to reduce inter-subject variability at the data level. Then, multi-constrained feature alignment (MCFA) is introduced, which iteratively constructs a kernel mapping space and then determines an optimized subspace to align both marginal and conditional distributions at the feature level under class structure and dispersion constraints. Moreover, in this iterative process of feature alignment, a selective pseudo-label update method is proposed to update the pseudo-labels of only the target samples with high classification confidence to realize more reliable conditional distribution alignment. Two benchmark datasets were used to verify the presented MCTLP. The results showed that MCTLP outperformed other existing methods, demonstrating its strong ability for cross-subject transfer. Full article

Unsupervised domain adaptation (UDA) remains challenged by an unstable target structure, pseudo-label noise, and heterogeneous transfer difficulty across domains. To address these issues, we propose Progressive Multi-View Graph Projection (PMGP), a two-stage framework that first learns transferable representations via source supervision, domain-adversarial training, and teacher–student consistency and then performs latent-space refinement through multi-view graph construction and projection learning. Specifically, three perturbation-induced views are considered for each sample: the original view, an input-space patch-masked view, and a representation-space feature-dimension masked view. After joint preprocessing with PCA and L2 normalization, PMGP constructs per-view affinity graphs by combining geometric neighborhood relations with pseudo-supervised semantic relations, and applies locality-preserving projection to learn a structure-aware shared subspace. In this subspace, target pseudo-labels are iteratively refined using source prototypes, target class centers, and progressive confidence filtering. Experiments on Office-Home, ImageCLEF-DA, and VisDA-2017 show that PMGP achieves competitive performance and stable behavior across different benchmark settings and backbone architectures. These results indicate that multi-view graph refinement provides an effective and interpretable way to improve target structure estimation and reduce pseudo-label error accumulation in UDA. Full article

Hyperspectral unmixing (HU) is fundamental for conducting quantitative analyses in remote sensing, yet existing methods face a persistent tradeoff between model performance and physical interpretability. Although deep learning models achieve superior performance, even “gray-box” models that incorporate physical constraints still suffer from an intrinsically opaque decision-making process, which hinders their trustworthiness in critical applications. To address this challenge, this paper introduces a theory-guided unmixing framework aimed at enhancing mechanistic interpretability called the sparse and subspace-attentive transformer unmixing network (SSTU-Net). Unlike heuristic architectures, SSTU-Net is rigorously derived from the first principles of sparse rate reduction (SRR) theory. Its core modules—the multi-head subspace self-attention (MSSA) and the iterative shrinkage-thresholding algorithm (ISTA)—directly implement the essential mathematical steps of information compression and sparsification within the SRR theory, respectively. Extensive experiments on both synthetic and real hyperspectral datasets demonstrate that SSTU-Net achieves competitive performance compared to representative state-of-the-art methods—including advanced autoencoder-based networks (e.g., CyCU-Net and DAAN) and recent transformer-based unmixing architectures (e.g., DeepTrans and MAT-Net)—while strictly adhering to theoretically predicted evolutionary trajectories. More importantly, a series of specifically designed structural interpretability validation experiments mechanistically confirm the theoretically predicted behaviors, such as layer-wise information compression, feature sparsification, and subspace orthogonalization. These results reveal the internal working mechanisms of SSTU-Net, validating the feasibility and significant potential of our principled theory-guided framework for developing high-performance and trustworthy intelligent models in remote sensing. Full article

In order to overcome the computational challenges associated with block preconditioners for Krylov subspace methods, particularly those arising from Schur complement systems, this paper proposes an improved new block (INB) preconditioner for solving 3 × 3 block saddle point problems. A detailed semi-convergence analysis of the iterative scheme induced by the INB preconditioner is provided. Moreover, the spectral properties of the preconditioned matrix are analyzed, revealing strong eigenvalue clustering around one. Efficient formulas for selecting quasi-optimal parameters are derived based on Frobenius-norm minimization. Extensive numerical experiments demonstrate that the proposed INB preconditioner significantly reduces iteration counts and CPU time compared with several existing block preconditioners. Full article

High-dimensional surrogate modeling with limited high-fidelity data poses a major challenge in uncertainty quantification. Classical supervised dimension reduction methods often fail in this setting due to insufficient accurate observations, while low-fidelity data are abundant but biased. In this work, we propose a Rotated Multi-Fidelity Gaussian Process (RMFGP) framework that enables reliable dimension reduction and surrogate construction under severe data scarcity. The proposed method integrates nonlinear multi-fidelity Gaussian process regression with sliced average variance estimation (SAVE) to iteratively identify informative input directions. Low-fidelity data are first used to extract coarse structural information, which is exploited to rotate the input space prior to multi-fidelity model training. Predictions generated by the trained RMFGP surrogate are then used to refine the dimension reduction, allowing accurate estimation of the central sufficient dimension reduction subspace even when high-fidelity data are scarce. A Bayesian active learning strategy based on predictive uncertainty is further incorporated to adaptively select new high-fidelity samples. Numerical examples, including stochastic partial differential equations, demonstrate that RMFGP significantly improves prediction accuracy, convergence, and uncertainty propagation compared to existing Gaussian process-based dimension reduction approaches, while requiring substantially fewer high-fidelity evaluations. Full article

This paper relies on orthogonal metric spaces related to cyclic self-mappings and some of their relevant properties. The involved binary relation is not symmetric, and then the term pseudo-orthogonality will be used for the relation used in the article to address the established results on cyclic self-mappings. Firstly, some orthogonal binary relations are given through examples to fix some ideas to be followed in the main body of the article. It is seen that the orthogonal elements of the orthogonal sets are not necessarily singletons. Secondly, “ad hoc” specific orthogonality binary relations are also described through examples related to the investigation of stability and controllability problems in dynamic systems. The main objective of this paper is to investigate the properties of cyclic single-valued self-mappings on the union of any finite number $p\ge 2$ of nonempty closed subsets of a metric space in a cyclic disposal under an “ad hoc” defined pseudo-orthogonality condition. Such a condition is defined on certain subsequences, referred to as pseudo-orthogonal sequences, rather than on the whole generated sequences under the self-mapping. It basically consists of a cyclic, in general iteration-dependent, contractive condition just for such subsequences which, on the other hand, are not forced as a constraint to be fulfilled by the whole sequences. Furthermore, the whole sequences in which those sequences are contained are allowed to be locally non-contractive or even locally expansive. The boundedness and the convergence properties of distances between pseudo-orthogonal subsequences and sequences are investigated under the condition that one of the subsets has a unique best proximity point to its adjacent subset in the cyclic disposal to which the pseudo-orthogonal subsequences converge. The pseudo-orthogonal metric subspace of the given metric space is proved to be complete although the whole metric space is not assumed to be complete. The pseudo-orthogonal element is seen to be a set of best proximity points, one per subset of the cyclic disposal, although it is not required for all the best proximity sets to be singletons. It is proved that the pseudo-orthogonal subsequences converge to a limit cycle, consisting of a best proximity point per subset of the cyclic disposal, which is also the pseudo-orthogonal element. The whole sequences are also proved to be bounded and the distances between their elements in adjacent subsets are also proved to converge to the distance between adjacent subsets. In the event that the metric space is a uniformly convex Banach space, it suffices that one of the subsets of the cyclic disposal be boundedly compact with its best proximity set being a singleton. In this case, the pseudo-orthogonal sequences converge to their best proximity set to their adjacent subset provided that such a best proximity set is a singleton. Full article

Sensor-less adaptive optics (SLAO) using stochastic parallel gradient descent (SPGD) offers a promising solution for wavefront correction in free-space optical communication (FSOC) systems, as it eliminates the need for conventional wavefront sensors. However, the standard SPGD algorithm’s convergence speed is limited, and it is prone to becoming trapped in local extrema, especially under complex, high-dimensional wavefront distortions in large-scale and dynamic FSOC systems, hindering its use in time-sensitive, high-precision scenarios. To address these limitations, we propose a novel Modal Stage SPGD (MSSPGD) algorithm which integrates subspace optimization techniques with the traditional SPGD algorithm. By projecting the control problem onto a reduced-dimensional Zernike modal subspace and adaptively expanding controlled modes number based on performance metric, our approach decomposes the high-dimensional optimization task into a coarse to fine search optimization problem, thereby accelerating convergence speed, reducing computational complexity, and enhancing robustness against local optima. Theoretical analysis and numerical simulations demonstrate that the proposed algorithm improves convergence speed, stability, and adaptability leading to more effective mitigation of turbulence-induced degradation in critical FSOC metrics. Experimental results further show that the MSSPGD algorithm achieves an approximately 25% reduction in iteration count compared to conventional SPGD. These enhancements prove that the algorithm highly suitable for real-time SLAO in demanding high-speed FSOC systems. Full article