Search Results (2,890)

Aerial robots are a well-established solution for exploration, monitoring, and inspection, thanks to their superior maneuverability and agility. However, in many environments, they risk crashing and sustaining damage after collisions. Traditional methods focus on avoiding obstacles entirely, but these approaches can be limiting, particularly in cluttered spaces or on weight- and computationally constrained platforms such as drones. This paper presents a novel approach to enhance drone robustness and autonomy by developing a path recovery and adjustment method for a high-speed collision-resilient aerial robot equipped with lightweight, distributed tactile sensors. The proposed system explicitly models collisions using pre-collision velocities, rates and tactile feedback to predict post-collision dynamics, improving state estimation accuracy. Additionally, we introduce a computationally efficient vector-field-based path representation that guarantees convergence to a user-specified path, while naturally avoiding known obstacles. Post-collision, contact point locations are incorporated into the vector field as a repulsive potential, enabling the drone to avoid obstacles while naturally returning to its path. The effectiveness of this method is validated through Monte Carlo simulations and demonstrated on a physical prototype, showing successful path following, collision recovery, and adjustment at speeds up to $3.7$$\mathrm{m}$/$\mathrm{s}$. Full article

In this review, we present a general framework for the construction of Kac–Moody (KM) algebras associated to higher-dimensional manifolds. Starting from the classical case of loop algebras on a circle ${\mathbb{S}}^1$, we extend the approach to compact and non-compact group manifolds, coset spaces, and soft deformations thereof. After recalling the necessary geometric background on Riemannian manifolds, Hilbert bases, and Killing vectors, we present the construction of generalized current algebras $\mathfrak{g}\left(\mathcal{M}\right)$, their semidirect extensions with isometry algebras, and their central extensions. We show how the resulting algebras are controlled by the structure of the underlying manifold, and we illustrate the framework through explicit realizations on $SU\left(2\right)$, $SU\left(2\right)/U\left(1\right)$, and higher-dimensional spheres, highlighting their relation to Virasoro-like algebras. We also discuss the compatibility conditions for cocycles, the role of harmonic analysis, and some applications in higher-dimensional field theory and supergravity compactifications. This provides a unifying perspective on KM algebras beyond one-dimensional settings, paving the way for further exploration of their mathematical and physical implications. Full article

In addition to the basic voltage vector modulation technique, virtual vectors can be generated through the discrete space vector modulation (DSVM) technique. Consequently, DSVM-based model predictive control (MPC) can achieve the reduction in current harmonics and torque ripples in permanent magnet synchronous machine (PMSM) drives. However, as the number of virtual candidate voltage vectors becomes excessively large, the computational burden increases significantly. This paper proposes an artificial neural network (ANN) control algorithm, in which massive input and output datasets generated by an existing DSVM-MPC algorithm are utilized for ANN offline training. In this way, the ANN can efficiently select the optimal voltage vector without enumerating all candidate voltage vectors, thereby reducing the heavy online computation of the DSVM-MPC controller and significantly reducing the computational burden. Finally, the effectiveness of the proposed ANN controller is validated. Full article

In this study, Cartan null curves connected via the Combescure transformation are investigated within the framework of Minkowski 3-space, and the necessary conditions for establishing such connections are derived. The relationships between the Frenet vectors and curvatures of these curve pairs are also analyzed. Furthermore, when a ruled surface generated by a Cartan null curve provides a solution to the Da Rios equation, the conditions under which the ruled surface generated was by the corresponding Cartan null curve, related through the Combescure transformation, also satisfies the equation. All obtained results are supported with illustrative examples. Full article

Background/Objectives: In computer graphics, virtual worlds are constructed and visualized through algorithmic processes. These environments are typically populated with objects defined by mathematical models, traditionally based on Euclidean geometry. However, there is increasing interest in exploring non-Euclidean geometries, which require adaptations of the modeling techniques used in Euclidean spaces. Methods: This paper focuses on defining parametric curves and surfaces within elliptic and hyperbolic geometries. We explore free-form splines interpreted as hierarchical motions along geodesics. Translation, rotation, and ruling are managed through supplementary curves to generate surfaces. We also discuss how to compute normal vectors, which are essential for animation and lighting. The rendering approach we adopt aligns with physical principles, assuming that light follows geodesic paths. Results: We extend the Kochanek–Bartels spline to both elliptic and hyperbolic geometries using a sequence of geodesic-based interpolations. Simple recursive formulas are introduced for derivative calculations. With well-defined translation and rotation in these curved spaces, we demonstrate the creation of ruled, extruded, and rotational surfaces. These results are showcased through a virtual reality application designed to navigate and visualize non-Euclidean spaces. Full article

This study presents a self-supervised learning framework for detecting frequency disturbances in power systems using high-resolution time series data. Employing data from the UK National Grid, we apply the Temporal Contrastive Self-Supervised Learning (TC-TSS) approach to learn task-agnostic embeddings from unlabelled 60-s rolling window segments of frequency measurements. The learned representations are then used to train four traditional classifiers, Logistic Regression (LR), Support Vector Machine (SVM), Multi-Layer Perceptron (MLP), and Random Forest (RF), for binary classification of frequency stability events. The proposed method is evaluated using over 15 million data points spanning six months of system operation data. Results show that classifiers trained on TC-TSS embeddings performed better than those using raw input features, particularly in detecting rare disturbance events. ROC-AUC scores for MLP and SVM models reach as high as 0.98, indicating excellent separability in the latent space. Visualisations using UMAP and t-SNE further demonstrate the clustering quality of TC-TSS features. This study highlights the effectiveness of contrastive representation learning in the energy domain, particularly under conditions of limited labelled data, and proves its suitability for integration into real-time smart grid applications. Full article

Reliable multilevel inverter IGBT modules require precise loss and heat management, particularly in severe traction applications. This paper presents a comprehensive modeling framework for three-level T-type neutral-point clamped (TNPC) inverters using a high-power Insulated Gate Bipolar Transistor (IGBT) module that combines model predictive control (MPC) with space vector pulse width modulation (SVPWM). The particle swarm optimization (PSO) algorithm is used to methodically tune the MPC cost function weights for minimization, while achieving a balance between output current tracking, stabilization of the neutral-point voltage, and, consequently, a uniform distribution of thermal stress. The proposed SVPWM-MPC algorithm selects optimal switching states, which are then utilized in a chip-level loss model coupled with a Cauer RC thermal network to predict transient chip-level junction temperatures dynamically. The proposed framework is executed in MATLAB R2024b and validated with experiments, and the SemiSel industrial thermal simulation tool, demonstrating both control effectiveness and accuracy of the electro-thermal model. The results demonstrate that the proposed control method can sustain neutral-point voltage imbalance of less than 0.45% when operating at 25% load and approximately 1% under full load working conditions, while accomplishing a uniform junction temperature profile in all inverter legs across different working conditions. Moreover, the results indicate that the proposed control and modeling structure is an effective and common-sense way to perform coordinated electrical and thermal management, effectively allowing for predesign and reliability testing of high-power TNPC inverters. Full article

The adoption of Interior Permanent Magnet Synchronous Motor (IPMSM) in Battery Electric Vehicle (BEV) and Plug-in Hybrid Electric Vehicle (PHEV) drives the need for innovative approaches to improve control performance and power conversion efficiency. This paper aims at evaluating advanced Model Predictive Control (MPC) strategies for IPMSM drives in a methodic comparison with the most widespread Field Oriented Control (FOC). Different extensions of direct Finite Control Set MPC (FCS-MPC) and indirect Continuous Control Set MPC (CCS-MPC) MPCs are considered and evaluated in terms of reference tracking performance, robustness, power efficiency, and complexity based on Matlab, Simulink™ simulations. Results confirm the inherent better control quality of MPCs over FOC in general and allow us to further identify some possible directions for improvement. Moreover, indirect MPCs perform better, but complexity may prevent them from supporting real-time implementation in some cases. On the other hand, direct MPCs are less complex and reduce inverter losses but at the cost of increased Total Harmonic Distortion (THD) and decreased robustness to parameters deviations. These results also highlight various trade-offs between different predictive control strategies and their feasibility for high-performance automotive applications. Full article

Accurate forecasts of the U.S. renewable energy consumption mix are essential for planning transmission upgrades, sizing storage, and setting balancing market rules. We introduce a Bayesian Dirichlet ARMA model (BDARMA) tailored to monthly shares of hydro, geothermal, solar, wind, wood, municipal waste, and biofuels from January 2010 through January 2025. The mean vector is modeled with a parsimonious VAR(2) in additive log ratio space, while the Dirichlet concentration parameter follows an intercept plus five Fourier harmonics, allowing for seasonal widening and narrowing of predictive dispersion. Forecast performance is assessed with a 61-split rolling origin experiment that issues twelve month density forecasts from January 2019 to January 2024. Compared with three alternatives (a Gaussian VAR(2) fitted in transform space, a seasonal naive approach that repeats last year’s proportions, and a drift-free ALR random walk), BDARMA lowers the mean continuous ranked probability score by 15 to 60 percent, achieves componentwise 90 percent interval coverage near nominal, and maintains point accuracy (Aitchison RMSE) on par with the Gaussian VAR through eight months and within 0.02 units afterward. These results highlight BDARMA’s ability to deliver sharp and well-calibrated probabilistic forecasts for multivariate renewable energy shares without sacrificing point precision. Full article

In this paper, we introduce fractal interpolation on complete semi-vector spaces. This approach is motivated by the requirements of the preservation of positivity or monotonicity of functions for some models in approximation and interpolation theory. The setting in complete semi-vector spaces does not requite additional assumptions but is intrinsically built into the framework. For the purposes of this paper, fractal interpolation in the complete semi-vector spaces $C^{+}$ and $L_p^{+}$ is considered. Full article

The forecasting of Drug-Drug Interactions (DDIs) is essential in pharmacology and clinical practice to prevent adverse drug reactions. Existing approaches, often based on neural networks and knowledge graph embedding, face limitations in modeling correlations among drug features and in handling complex BioKG relations, such as one-to-many, hierarchical, and composite interactions. To address these issues, we propose Rot4Cap, a novel framework that embeds drug entity pairs and BioKG relationships into a four-dimensional vector space, enabling effective modeling of diverse mapping properties and hierarchical structures. In addition, our method integrates molecular structures and drug descriptions with BioKG entities, and it employs capsule network–based attention routing to capture feature correlations. Experiments on three benchmark BioKG datasets demonstrate that Rot4Cap outperforms state-of-the-art baselines, highlighting its effectiveness and robustness. Full article

Knowledge Tracing aims to assess students’ mastery of knowledge concepts in real time, playing a crucial role in providing personalized learning services in intelligent tutoring systems. In recent years, researchers have attempted to introduce Neural Architecture Search (NAS) into knowledge tracing tasks to automatically design more efficient network structures. However, existing NAS-based methods for Knowledge Tracing suffer from excessively large search spaces and slow search efficiency, which significantly constrain their practical applications. To address these limitations, this paper proposes an Adaptive Neural Architecture Search framework based on Transformers for KT, called ANT-KT. Specifically, we design an enhanced encoder that combines convolution operations with state vectors to capture both local and global dependencies in students’ learning sequences. Moreover, an optimized decoder with a linear attention mechanism is introduced to improve the efficiency of modeling long-term student knowledge state evolution. We further propose an evolutionary NAS algorithm that incorporates a model optimization efficiency objective and a dynamic search space reduction strategy, enabling the discovery of high-performing yet computationally efficient architectures. Experimental results on two large-scale real-world datasets, EdNet and RAIEd2020, demonstrate that ANT-KT significantly reduces time costs across all stages of NAS while achieving performance improvements on multiple evaluation metrics, validating the efficiency and practicality of the proposed method. Full article

The pure states of two-qubit quantum systems are described by a four-dimensional vector of complex numbers, and unitary operators transferring a two-qubit quantum system from one state to another have the form of a $4\times 4$ matrix with complex elements. This fact brings to mind the idea of studying the spaces of four-dimensional numbers with complex components. Moreover, the results obtained by the authors for four-dimensional numbers with real components inspire some optimism. In this paper we construct four-dimensional spaces of complex numbers by analogy with four-dimensional spaces of real numbers. Each four-dimensional number is mapped to a matrix formed from its components and it is proved that the constructed mapping is a bijection and a homomorphism. In the space of four-dimensional numbers of the eight basis elements, half are real and half are imaginary. The presence of such symmetry distinguishes these spaces from the space of quaternions, in which one basis element is real and the rest are imaginary. The symmetry of the basis numbers makes these spaces a natural generalization of one-dimensional and two-dimensional (complex) algebra. The conditions under which the corresponding matrices are gates for two-qubit quantum systems are defined. The notion of a unitary state of a two-qubit quantum system is introduced, to which various gates from commutative groups of gates correspond. It is shown that any gate of a unitary state transforms a unitary state into a unitary state and a non-unitary state into a non-unitary state. Almost all gates used in the construction of quantum circuits, in particular H, SWAP, CX, CY, and CZ, have the same properties. The problem of searching for a gate that transfers a quantum system from one unitary state to another unitary state has been solved. Thus, with the help of four-dimensional spaces of complex numbers it was possible to construct whole classes of two-qubit gates, which opens new possibilities for the construction of quantum algorithms. The results obtained have important theoretical and practical implications for quantum computing. Full article

We discuss the complex-analytic subsets of the moduli spaces of rank 2 vector bundles on a classical Hopf surface formed by irregular bundles. We stratify the set of irregular bundles by weight (and irregular profiles). We provide the topological result (vanishing of higher cohomology groups) on the part of the moduli spaces parameterizing regular bundles. Full article

Breast tissue-mimicking phantoms are essential tools for validating microwave imaging systems designed for early breast cancer detection. In this work, we report the fabrication and comprehensive characterization of oil-in-gelatin phantoms emulating normal, benign, and malignant breast tissues. The phantoms were manufactured with controlled mixtures of kerosene, safflower oil, and gelatin, and their dielectric properties were experimentally evaluated using a free-space transmission method with a Vector Network Analyzer across the 100 MHz–10 GHz range. Results demonstrated significant contrast in permittivity and conductivity among the different tissue types, consistent with values reported in the literature. Long-term stability was confirmed for up to six months under controlled storage. Additional structural and thermal characterization was performed using Fourier transform infrared spectroscopy (FTIR), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA), providing insight into molecular composition and thermal response. The proposed method enables reproducible, low-cost, and stable phantom fabrication, offering reliable tissue models to support experimental validation and optimization of microwave-based breast cancer detection systems. Full article