This study presents an advanced AI-Adaptive Hilbert and Logistic Image Encryption Mechanism (HL-IEM) that combines an Adaptive Feed-Forward Neural Network (FNN), a Logistic Chaotic Map, and Hilbert Curve Block Scrambling to achieve robust, lightweight, and content-aware image security. The FNN operates on image features such as mean intensity, variance, entropy, and edge density, and accordingly generates optimised chaotic parameters that control both pixel-level diffusion via the Logistic Map and adaptive block-level permutation via the Hilbert Curve. This collaboration between AI-driven chaotic control and nonlinear permutation-diffusion ensures strong key sensitivity, high randomness, and complete decorrelation of adjacent pixels. Experimental evaluation across standard test images (Peppers, Tree, Airplane, and House) demonstrates near-ideal information entropy (7.9488-7.9932), correlation coefficients close to zero after encryption, NPCR above 99.83%, and UACI around 32.90 to 33.78%. The MSE values range from 8125 to 8205, and the PSNR values range from 9.03 to 9.08 dB, indicating very high image quality. The encryption and decryption times are around 1second for [Formula: see text] images, indicating that the technique can be used in real-time scenarios in IoT and multimedia environments. The proposed method increases computational load only slightly and has been confirmed to be quite resistant to statistical, differential, and brute-force attacks. These findings establish the AI-adaptive HL-IEM as a highly secure, efficient, and scalable image encryption solution suitable for both civilian and defence-grade communication systems.

Semantic indexing ensures better organization and optimized searching of heterogeneous, autonomous, and distributed data sources. This approach leverages meaning and context rather than just keywords to better manage the increasing volume, complexity, and heterogeneity of modern data, enabling precise searching, optimized integration, and improved interoperability between domains. Several approaches to semantic indexing are available: ontology-based indexing, machine learning and automated semantic annotation of data sources. However, the main challenge remains scaling up. This article focuses on a conceptual framework designed for scalable semantic indexing of data sources based on a structured peer-to-peer architecture adapted for managing a very large number of nodes, Hilbert curve renowned for its preservation of semantic affinity while scaling, hypercube structure with its efficient diffusion algorithm, semantic annotation of data sources based on keywords, as well as machine learning techniques, in particular, multidimensional data analysis. An illustrative exploratory example of the Meta Skills semantic class is presented to outline the proposed architecture. This study proposes a conceptual and exploratory framework for large-scale semantic indexing of data sources. The proposed approach has not yet been implemented or validated on a large scale; its objective is to provide an initial structured model to serve as a basis for future empirical research.

The detection and identification of unmanned aerial vehicles (UAVs) using radio frequency (RF) signals becomes particularly challenging in congested spectral environments, where conventional approaches relying solely on spectral characteristics often prove limited. This work introduces a novel technique for both UAV detection and classification based on temporal representations derived directly from the envelope of received RF signals. The proposed system follows a two-stage architecture: first, binary detection of UAV presence in a given RF channel, and second, identification of the specific UAV model among several commercial platforms. For the first stage, two signal representation methodologies are employed—Gramian Angular Fields and Hilbert curves—both generated from short-time RF windows and subsequently used as inputs to convolutional neural networks. Experimental evaluation demonstrates that the detection stage achieves accuracy rates exceeding 94% for the non-UAV class and approaching 99% for the UAV class with both approaches. In the identification stage, the system attains an accuracy above 90% for most considered UAV models, reaching up to 100% for certain platforms. These results confirm the effectiveness of the envelope-based approach for analyzing UAV-related RF signals.

This paper reports on a novel transducer for wireless biochemical sensing. The bilayer transducer consists of a fractal piezoelectric membrane, laminated with a pH-sensitive chemo-mechanical hydrogel. The proposed scheme utilizes the piezoelectric element as a wireless transducer and the phase transition behavior of hydrogels as a sensing element. Notably, the fractal design on the piezoelectric membrane enhances frequency response and linearity by employing a periodically repeated pore architecture. As a basis of the pore, a modified Hilbert space-filling curve is used. By laminating a pH-sensitive hydrogel onto a fractal-porous piezoelectric thin film, the overall transducer curls inward or outward, depending on the environmental pH (e.g., pH = 4, 8, and 12). The curvature exhibits a sensitivity of 10.5°/pH, yielding accordant ultrasound responses under excitation. The measured voltage outputs from an ultrasonic receiver were 0.393, 0.341, and 0.250 mV/cm<sup>2</sup> for curvature angles of 30°, 60°, and 120°, respectively. Overall pH sensitivity was 0.017 mV/cm<sup>2</sup>/pH. Ultimately, the biochemical sensing principle using a novel bilayer ultrasound transducer suggests a simple, low-cost, battery-less, and long-range wireless readout system as compared to traditional biochemical sensing.

Last-mile delivery companies can face demand surges where large-volume order requests exceed daily courier capacity. In such cases fast and robust feasibility-first planning becomes more practical and valuable than building optimal routes. This paper proposes a hierarchical, computationally feasible decomposition pipeline that produces shift-feasible clusters under a strict shift-duration limit using travel-time-based duration estimates. While decomposition methods for large-scale VRPs are well established, they typically remain oriented toward route-construction quality within a single operational day or toward balancing customer counts, demand, or Euclidean territory partitions. In contrast, the proposed method targets a different decision problem: rapid feasibility-first strategic capacity planning for one-time extreme demand surges, where the primary requirement is to estimate, within seconds, a conservative upper bound on the number of courier shifts under a strict shift-duration limit. When end-to-end latency is evaluated from raw geographic points, including distance-matrix preparation for monolithic baselines, the proposed pipeline becomes 187 to 1315 times faster than matrix-based monolithic optimization on the common benchmark sizes. Methodologically, the contribution lies in combining (i) topology-preserving spatial linearization with a Hilbert Space-Filling Curve, (ii) adaptive greedy microclustering driven by empirical travel-time quantiles, and (iii) lexicographic dynamic-programming merge that minimizes the number of shifts first and total travel time second. This yields a planning-oriented decomposition mechanism that is distinct from classical route-quality-centered hierarchical VRP approaches.

The present study investigates the influence of Fused Deposition Modelling (FDM) process parameters on the mechanical properties and surface quality of multi-material PLA-ABS Bi-layer Laminate Structures fabricated at elevated printing speeds. A Taguchi L9 orthogonal array was used to evaluate the effects of printing speed (150–250 mm/s), layer height (0.1–0.3 mm), and infill pattern (concentric, octagram spiral, and Hilbert curve) on tensile properties and surface roughness. The results show that a printing speed of 150 mm/s, a layer height of 0.1 mm, and concentric infill provided optimal mechanical performance, yielding a Young’s modulus of 1252.29 MPa, an ultimate tensile strength of 42.17 MPa, and an elongation at break of 5.79%. Surface roughness analysis indicated the minimum roughness (R a = 3.4 µm) at a printing speed of 250 mm/s and a layer height of 0.2 mm using concentric infill. Statistical evaluation using mean effect plots, signal-to-noise ratios, and ANOVA revealed that layer height predominantly governs surface quality, while infill pattern and printing speed significantly influence tensile behaviour. Optical fractography and scanning electron microscopy showed that fracture initiation occurred at interlayer interfaces and inter-raster voids. Well-bonded specimens exhibited ductile micro-void coalescence, whereas poorly bonded samples failed by interlayer separation and brittle fracture propagation. These findings demonstrate that appropriate selection of layer height and infill pattern enables rapid fabrication of PLA-ABS Bi-layer Laminate components with improved mechanical performance and surface finish.

We propose a flexible and robust nonparametric framework for testing spatial dependence in two- and three-dimensional random fields. Our approach involves converting spatial data into one-dimensional time series using space-filling Hilbert curves. We then apply ordinal pattern-based tests for serial dependence to this series. Because Hilbert curves preserve spatial locality, spatial dependence in the original field manifests as serial dependence in the transformed sequence. The approach is easy to implement, accommodates arbitrary grid sizes through generalized Hilbert ("gilbert") curves, and naturally extends beyond three dimensions. This provides a practical and general alternative to existing methods based on spatial ordinal patterns, which are typically limited to two-dimensional settings.

Abstract We investigate tensor network simulations of the two-dimensional (2D) Hubbard model by mapping the lattice onto a one-dimensional chain using space-filling curves. In particular, we focus on the Hilbert curve, whose locality-preserving structure minimizes the range of effective interactions in the mapped model. This enables a more compact matrix product state representation compared to conventional snake mapping. Through systematic benchmarks, we show that the Hilbert curve consistently yields lower ground-state energies at fixed bond dimension, with the advantage increasing for larger system sizes and in physically relevant interaction regimes. Our implementation reaches clusters up to 32 × 32 sites with open and periodic boundary conditions, delivering reliable ground-state energies and correlation functions in agreement with established results, but at significantly reduced computational cost. These findings establish space-filling curve mappings, particularly the Hilbert curve, as a powerful tool for extending tensor-network studies of strongly correlated 2D quantum systems beyond the limits accessible with standard approaches.

Currently, coil misalignment is recognized as one of the primary factors limiting the transmission efficiency of wireless power transfer (WPT) systems, presenting a substantial barrier to the large-scale adoption of wireless power transfer. To enhance transmission efficiency under misalignment, mitigate the impacts of misalignment, and increased transmission distance of wireless power transfer systems, research on Hilbert fractal curves in related fields was referenced, mutual inductance expressions for coils with Hilbert-extended structures and conventional coils were derived based on their mathematical formulations, and the potential advantages of Hilbert curves in wireless power transfer applications were analyzed. Supported by extensive simulation outcomes, a fractal coil incorporating a Hilbert structure was designed without altering coil manufacturing costs. The transmission performance advantages of this coil were investigated through simulations. A WPT system verification platform utilizing an LCC-S circuit was constructed, where 300W power and efficiency tests were conducted under relatively consistent ZVS conditions for both coil types. Experimental results across varying transmission distances and misalignment distances were obtained. The results demonstrate that the proposed coils comprehensively optimize the power transfer capability of conventional coils, delivering more stable output power and improving the transmission efficiency by over 10% (up to 24%).

HMSNet: Hilbert curve enhanced Mamba for real-time semantic segmentation

Abstract This paper presents the development and implementation of a 4-port MIMO antenna based on a combination of a Hilbert curve fractal and a reactive load implemented via an open-circuited stub. The integration of these techniques results in a highly compact array with a wide operating bandwidth, extending from 2.3 GHz to 5.8 GHz. This covers the 2.4 GHz ISM band and the 5G New Radio (NR) bands N41, N77, N78, and N79. The total array dimensions are 25 mm x 36 mm, equivalent to 0.18λ0×0.26λ0 at the lower cutoff frequency. The minimum separation between elements is 3 mm, approximately 0.02λ0, which is a very small distance between radiators. However, by incorporating an electromagnetic barrier and giving galvanic continuity, also implemented with a Hilbert curve on the ground plane, an isolation ranging from 15 dB to over 20 dB is achieved across the entire bandwidth, with a peak gain of 1.8 dB. Furthermore, the use of the open-circuited stub stabilizes the antenna's impedance behavior, causing the reactive component to approach 0 Ω, while the real part stabilizes within a threshold close to 50 Ohms, significantly increasing the bandwidth. The final result is a compact 4-port MIMO antenna featuring high isolation, an Envelope Correlation Coefficient (ECC) below 0.05 across the entire range, a Diversity Gain (DG) close to 10, and a stable Total Active Reflection Coefficient (TARC) below -10 dB throughout the operating bandwidth.I.

Abstract We present Guangqi , a new 2D, finite-volume radiation hydrodynamics code designed for high-performance astrophysical simulations. The code simultaneously resolves the hydrodynamic equations for complex equations of state (EoS) and implicit radiation transport under the flux-limited-diffusion approximation. Written in Fortran and parallelized via the Message Passing Interface, Guangqi supports analytic hydrogen and helium EoS under the assumption of local thermal and chemical equilibrium. The framework is compatible with both Cartesian and spherical-polar geometries—utilizing nonuniform grid spacing—and incorporates static mesh refinement and adaptive mesh refinement to optimize computational efficiency. To address the inherent challenges of angular momentum conservation in spherical-polar coordinates, we implement a robust and consistent “passive scalar angular momentum algorithm.” Domain decomposition is managed through both Z-order and Hilbert space-filling curves to ensure scalability. The code has been rigorously verified against a suite of standard benchmarks and newly designed test cases specifically intended to diagnose the nonlinear coupling between gas dynamics, intricate EoS, radiation transport, and angular momentum conservation.

Botnet detection remains a perennial and critical challenge in cybersecurity. As long as the internet exists, threat actors will devise new ways to create and disguise these malicious networks, making the development of robust detection methods a task that will never be obsolete. Traditional approaches, relying on rigid signatures and manual feature engineering, are often locked in a reactive cycle. A more critical limitation is their poor generalization; models trained on known botnets frequently fail to detect novel, unseen threats, rendering them vulnerable in real-world scenarios. This paper introduces a robust framework that significantly enhances botnet detection by overcoming these limitations. We propose a novel methodology that combines advanced feature engineering, such as octet splitting for IP addresses, with a sophisticated representation learning technique using the Hilbert space-filling curve to transform network flows into 2D images. This approach preserves data locality and eliminates the noise introduced by traditional zero-padding. Furthermore, we address the critical issue of class imbalance using a combination of SMOTE, a weighted sampler, and Focal Loss to focus the model on more challenging samples. To rigorously evaluate the model's real-world applicability, we employed a challenging cross-scenario validation strategy, training the model on the Murlo botnet (Scenario 8) and testing it on the completely unseen Rbot botnet (Scenario 10) from the publicly available CTU-13 dataset. Our proposed model achieved an outstanding accuracy of 98.34% and a weighted F1-score of 98.38%, demonstrating a remarkable ability to generalize to novel botnet attacks. This result validates our approach and highlights the superiority of learned, spatially-aware representations over traditional models, which failed to detect the unseen botnet. Our work presents a significant step towards creating more adaptive and resilient intrusion detection systems capable of handling novel, unseen botnet families.

An image encryption scheme based on an improved Hilbert curve and a novel 4D hyper-chaotic system

Performance analysis of multiport hilbert curve fractal antenna in mid-band applications

Alzheimer’s Disease (AD) is an advanced brain illness that affects millions of individuals across the world. It causes gradual damage to the brain cells, leading to memory loss and cognitive dysfunction. Although Magnetic Resonance Imaging (MRI) is widely used in AD diagnosis, the existing studies rely solely on the visual representations, leaving alternative features unexplored. The objective of this study is to explore whether MRI sonification can provide complementary diagnostic information when combined with conventional image-based methods. In this study, we propose a novel dual-stream multimodal framework that integrates 2D MRI slices with their corresponding audio representations. MRI images are transformed into audio signals using a multi-scale, multi-orientation Gabor filtering, followed by a Hilbert space-filling curve to preserve spatial locality. The image and sound modalities are processed using a lightweight CNN and YAMNet, respectively, then fused via logistic regression. The experimental results of the multimodal achieved the highest accuracy in distinguishing AD from Cognitively Normal (CN) subjects at 98.2%, 94% for AD vs. Mild Cognitive Impairment (MCI), and 93.2% for MCI vs. CN. This work provides a new perspective and highlights the potential of audio transformation of imaging data for feature extraction and classification.

Image security is vital in sectors such as healthcare, defence, finance, and personal data exchange, where breaches of image integrity can result in severe consequences. To address this challenge, we propose a novel image encryption framework. It combines a Fractal-Fibonacci diffusion process based on the Hilbert curve, recursive scrambling guided by chaotic sequences, and a new chaotic map entitled the Two Dimensional Cosine Power Sine Coupled Map (2D-CPSCM). These components enhance randomness and ensure maximum efficiency, resistance against cryptographic attacks. The proposed two-dimensional chaotic system exhibits positive Lyapunov exponents and superior statistical properties compared to traditional systems, as demonstrated by high sample entropy, permutation entropy, and Kolmogorov entropy, confirming its hyperchaotic behaviour. The encryption system has been evaluated using extensive simulations on benchmark images. The findings demonstrate strong key sensitivity, with an entropy of 7.9994, Number of Pixel Change Rate (NPCR) of 99.6%, Unified Average Changing Intensity (UACI) of 33.47%, and Number of Bit Change Rate (NBCR) of 50%. Additionally, Structural Similarity Index Metric (SSIM) and Visual Information Fidelity (VIF) values of 1 between input and decrypted images guarantee successful decryption, whereas low Peak Signal to Noise Ratio (PSNR), SSIM, and VIF between input and encrypted images reduce information leakage. The superior security, resilience, and robustness of the 2D-CPSCM based approach against statistical, noise, and cropping attacks highlights its potential for safe multimedia transmission and useful cryptographic applications.

Autonomous driving relies on accurate and reliable perception particularly in mixed traffic scenarios. In such complex environments including vehicles, pedestrians, barriers, and significant occlusions occur, degrading the quality of information collected by LiDAR and cameras. Therefore, current multimodal sensor fusion frameworks face difficulties in capturing long-range dependencies in point clouds and integrating information from sensors of different quality, which leads to inaccurate localization and object misclassification. To address these issues, we propose SMDFusion, a novel multimodal framework that effectively fuses LiDAR features, image frequency features, and depth information. Specifically, a Sparse-Mamba (SMM) module is introduced to capture long-range dependencies in sparse voxel features via Hilbert curve serialization and state-space modeling; a Depth-guided Frequency Enhancement (DFE) module leverages wavelet decomposition to refine image feature representations; and a Dynamic Gated Multimodal Fusion (DGMF) module adaptively models spatial, channel, and modality interactions for robust fusion. In addition, a distribution classification loss is designed to optimize the decision boundaries and mitigate misclassification among visually similar categories. Experiments on the large-scale nuScenes benchmark demonstrate that SMDFusion achieves 74.6% NDS and 71.9% mAP on the test set without test-time augmentation or model ensemble, while ablation studies further validate the contribution of each component.

ABSTRACT Mechanical‐Sensing Multifunctional Integrated System (MSMIS) that combines comfort and protection is essential for intelligent wearables. However, thickness constraints significantly limit the development of multifunctional metamaterials. While 2D metamembrane sensors provide sensitivity and conformability, they compromise energy absorption and multistage deformation in the vertical dimension. Here, we present a multifunctional sandwich architecture using mechanical metamaterials as facing layers. This design ensures consistent adherence to human movement while preventing saddle‐shaped deformation under out‐of‐plane loads. By maintaining the wearable device's thickness, we employed a self‐similar mathematical Hilbert curve structure as the core, which demonstrates excellent two‐stage load‐bearing capacity. This multi‐stage capacity ensures the first‐stage modulus remains below the human comfort level (0.1 MPa), while the second‐stage modulus increases by 510 times, achieving high load‐bearing and energy absorption performance under large deformation. Subsequent impact experiments and cross‐scale analyses further demonstrate the broad application potential of this mechanical‐sensing integrated structure, enabling real‐time monitoring of knees, elbows, and even fingers. Finally, by integrating machine learning, gesture recognition capabilities are achieved. This innovative design strategy opens up new possibilities for developing multi‐functional mechanical‐sensing integrated structures.

Advances in metamaterials, additive manufacturing, and computational design have enabled significant progress in airborne sound absorption. However, most absorbers still rely on two conventional mechanisms, i.e., friction-induced viscous loss and pressure-fluctuation-induced thermal loss, leaving their thickness constrained by the Rozanov bound. Here, we investigate an acoustic metamaterial based on a single three-dimensional Hilbert curve, designed to achieve sound absorption beyond this theoretical limit. The Hilbert curve forms continuous, tightly spaced winding channels whose geometry enables laminar flow-like shear dissipation. Experimental, numerical, and theoretical results demonstrate that with an optimal slit width close to the viscous boundary layer thickness, the actual thickness can be approximately 86% of the calculated Rozanov bound. This finding suggests a dissipation mechanism distinct from classical porous and resonator-based absorbers, opening different avenues for ultra-thin broadband sound absorbers.