Search Results (120)

Some properties on large contractions in metric spaces are proven. In particular, such contractions are proven to be asymptotically regular. In addition, if the metric space is complete, then the sequences that they generate are bounded, Cauchy, and convergent to a unique fixed point. Also, cyclic large contractions are an area of focus. It is proven that, if subsets of the cyclic disposal are nonempty closed and they intersect, all the sequences are bounded and Cauchy, and they converge to a unique fixed point located in the intersection of such subsets if the metric space is complete. If the subsets have a pair-wise empty intersection, then the boundedness of such sequences is proven without the need to assume the boundedness of the subsets in the cyclic disposal. The convergence of the sequences to a unique limit cycle of best proximity points, with one per subset in the cyclic disposal, is proven provided that the metric space is complete and that one of such subsets is boundedly compact with a singleton best proximity set. For that property to hold, it is not assumed that the remaining best proximity points are necessarily singletons. It has also been proven that all the subsequences contained within each of the subsets are Cauchy and they converge to a unique best proximity point, even if the corresponding best proximity sets is not a singleton. Furthermore, the hypothesis that one of the best proximity sets between adjacent subsets is a singleton can be weakened for any particular cyclic large contraction. Later on, eventual perturbations of the cyclic large self-mappings in normed spaces are discussed. If the norm of the perturbation additive operator is small enough, it is proven that the perturbed cyclic self-mapping maintains the property of being a cyclic large contraction associated with the unperturbed nominal cyclic large contraction. The maximum upper-bound of the perturbed operator ensures that such a property is given in an explicit manner. Full article

Discovering the compactness properties in generalized-type metric spaces opens up a fascinating area of research. The present study tries to develop a theoretical framework for compactness with key properties in the recently developed interval metric space. This work begins with explaining the covers and open covers to define compact interval metric spaces and their main features. Next, a similar definition of compactness using the finite intersection property is introduced. Then, the famous Heine–Borel theorem for compactness is extended in the case of interval metric spaces. Also, the concepts of sequential-type compactness and Bolzano–Weierstrass (BW)-type compactness for interval metric spaces are introduced with their equivalency relationship. Finally, the notion of total boundedness in interval metric spaces and its connection with compactness is introduced, providing new insights into these mathematical concepts. Full article

We characterize the upper semicontinuous representability of a semiorder ≺ as an interval order (namely, by a pair $(u,v)$ of upper semicontinuous real-valued functions) on a topological space with a countable basis of open sets, where one of the representing functions is a one-way utility for the characteristic weak order ${\prec }^0$ associated with the semiorder. Such a description generalizes the upper semicontinuous threshold representation. To this end, we introduce a suitable upper semicontinuity condition concerning a semiorder, namely strict upper semicontinuity. We further characterize the mere existence of an upper semicontinuous one-way utility for this characteristic weak order, with a view to the identification of maximal elements on compact metric spaces. Full article

Over the past two decades, Light Detection and Ranging (LiDAR) technology has evolved from early National Aeronautics and Space Administration (NASA)-led airborne laser altimetry into commercially mature systems that now underpin vegetation remote sensing across scales. Continuous advancements in laser engineering, signal processing, and complementary technologies—such as Inertial Measurement Units (IMU) and Global Navigation Satellite Systems (GNSS)—have yielded compact, cost-effective, and highly sophisticated LiDAR sensors. Concurrently, innovations in carrier platforms, including uncrewed aerial systems (UAS), mobile laser scanning (MLS), Simultaneous Localization and Mapping (SLAM) frameworks, have expanded LiDAR’s observational capacity from plot- to global-scale applications in forestry, precision agriculture, ecological monitoring, Above Ground Biomass (AGB) modeling, and wildfire science. This review synthesizes LiDAR’s cross-domain capabilities for the following: (a) quantifying vegetation structure, function, and compositional dynamics; (b) recent sensor developments encompassing ALS discrete-return ${(ALS}_D)$, and ALS full-waveform $\left({ALS}_{FW}\right)$, photon-counting LiDAR (PCL), emerging multispectral LiDAR (MSL), and hyperspectral LiDAR (HSL) systems; and (c) state-of-the-art data processing and fusion workflows integrating optical and radar datasets. The synthesis demonstrates that many LiDAR-derived vegetation metrics are inherently transferable across domains when interpreted within a unified structural framework. The review further highlights the growing role of artificial-intelligence (AI)-driven approaches for segmentation, classification, and multitemporal analysis, enabling scalable assessments of vegetation dynamics at unprecedented spatial and temporal extents. By consolidating historical developments, current methodological advances, and emerging research directions, this review establishes a comprehensive state-of-the-art perspective on LiDAR’s transformative role and future potential in monitoring and modeling Earth’s vegetated ecosystems. Full article

Continuous-wave magnetrons continue to offer the highest efficiency, lowest cost per watt, and greatest compactness among high-power microwave sources, making them attractive for industrial, scientific, and defense applications. Emerging missions, particularly space solar power systems, industrial microwave heating, and accelerators, demand significantly enhanced performance metrics, including high DC-to-RF efficiency, thermal stability, ultra-low phase noise, and precise phase controllability for coherent operation. To satisfy the critical requirement for high power, low-cost microwave sources with high spectral purity, extensive research has focused on injection-locking techniques, external phase/frequency modulation methods, and large-scale coherent power combining. This paper reviews the fundamental characteristics of CW magnetrons, recent advances in injection-locked magnetron transmitters, power-combining systems employing multiple injection-locked magnetrons, magnetron-based phased-array systems, and emerging applications. Finally, the challenges and promising development directions for next-generation CW magnetrons are discussed. Full article

Fine-grained building function identification (BFI) is essential for sustainable urban development, land-use analysis, and data-driven spatial planning. Recent progress in fully supervised semantic segmentation has advanced multimodal BFI; however, most approaches still rely on static fusion and lack explicit multi-scale alignment. As a result, they struggle to adaptively integrate heterogeneous inputs and suppress cross-modal interference, which constrains representation learning. To overcome these limitations, we propose BuildFunc-MoE, an adaptive multimodal Mixture-of-Experts (MoE) network built on an effective end-to-end Swin-UNet backbone. The model treats high-resolution remote sensing imagery as the primary input and integrates auxiliary geospatial data such as nighttime light imagery, DEM, and point-of-interest information. An Adaptive Multimodal Fusion Gate (AMMFG) first refines auxiliary features into informative fused representations, which are then combined with the primary modality and passed through multi-scale Swin-MoE blocks that extend standard Swin Transformer blocks with MoE routing. This enables fine-grained, dynamic fusion and alignment between primary and auxiliary modalities across feature scales. BuildFunc-MoE further introduces a Shared Task-Expert Module (STEM), which extends the MoE framework to share experts between the main BFI task and auxiliary tasks (road extraction, green space segmentation, and water body detection), enabling parameter-level transfer. This design enables complementary feature learning, where structural and contextual information jointly enhance the discrimination of building functions, thereby improving identification accuracy while maintaining model compactness. Experiments on the proposed Wuhan-BF multimodal dataset show that, under identical supervision, BuildFunc-MoE outperforms the strongest multimodal baseline by over 2% on average across metrics. Both PyTorch and LuoJiaNET implementations validate its effectiveness, while the latter achieves higher accuracy and faster inference through optimized computation. Overall, BuildFunc-MoE offers a scalable solution for fine-grained BFI with strong potential for urban planning and sustainable governance. 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

Accurate characterization of rail corrugation is essential for the operation and maintenance of urban rail transit. To enhance the representation capability for rail corrugation, this study proposes a sound–vibration feature fusion method based on Laplacian manifold learning. The method constructs a multidimensional feature space using real-world acoustic and vibration signals measured from metro vehicles, introduces a Laplacian manifold structure to capture local geometric relationships among samples, and incorporates inter-class separability into traditional intra-class compactness metrics. Based on this, a comprehensive feature evaluation index L_r is developed to achieve adaptive feature ranking. The final fusion indicator, LWVAF, is generated through weighted feature integration and used for rail corrugation characterization. Validation on in-service metro line data demonstrates that, after rail grinding, LWVAF exhibits a more pronounced reduction and higher sensitivity to changes compared with individual acoustic or vibration features, reliably reflecting improvements in rail corrugation. The results confirm that the proposed method maintains strong robustness and physical interpretability even under small-sample and weak-label conditions, offering a new approach for sound–vibration fusion analysis and corrugation evolution studies. Full article

In urban underground space construction using shield tunnelling, the geological conditions ahead of the tunnel face are often uncertain. Without timely and accurate classification of the ground type, mismatches in operational parameters, uncontrolled costs, and schedule risks are likely to occur. Using observations from an earth pressure balance (EPB) project on an urban railway, a data-driven classification framework is developed that integrates shield tunnelling operating measurements with physically derived quantities to discriminate among soft soil, hard rock, and mixed strata. Principal component analysis (PCA) is performed on the training set, followed by a systematic comparison of tree-based classifiers and hyperparameter optimization strategies to explore the attainable performance. Under unified evaluation criteria, a categorical bosting (CatBoost) model optimized by a Nevergrad combination strategy (NGOpt) attains the highest test accuracy of 0.9625, with macro-averaged precision and macro-averaged recall of 0.9715 and 0.9716, respectively. To mitigate optimism from single-point estimates, stratified bootstrap intervals are reported for the test set. A Monte Carlo experiment applies independent perturbations to the PCA-transformed features, producing low label-flip rates across the three classes, with only minor changes in probability calibration metrics, which suggests consistent decisions under sensor noise and sampling bias. Overall, within the scope of the considered EPB project, the study delivers a compact workflow that demonstrates the feasibility of uncertainty-aware ground-type classification and provides a methodological reference for developing decision-support tools in underground tunnel construction. Full article

We quantified how exhibit design and routine management shape behavior and space use in captive harbor seals (Phoca vitulina). Using a species-specific ethogram, scan sampling and focal follows on adult females housed in a modern zoo exhibit, we estimated time budgets, mapped space use across depth-defined zones, and modeled behavior sequences as first-order transition networks. Locomotion dominated activity (swimming/active travel), with resting and enrichment-related behaviors next most frequent; social and play behaviors occurred at low but non-negligible rates. Seals showed clear depth preferences, concentrating active swimming in deeper zones and using liminal/shallow areas for rest. Transition graphs revealed stable, low-entropy loops (e.g., swim → turn/pace → swim) consistent with repetitive locomotor routines, while enrichment and feeding windows temporarily diversified sequences and increased exploration. Overall, integrating time budgets with Markov-style transition analysis and spatial heatmaps provides a compact welfare-oriented dashboard: it identifies where exhibit depth and refuge availability support positive behavioral diversity, flags repetitive cycles as targets for enrichment, and offers actionable metrics to evaluate husbandry changes over time. Full article

In this study, we investigate a magnetically levitated electromagnetic vibration energy harvester (EMEH), in which a movable permanent magnet levitates between two fixed magnets with like poles facing the central magnet. We develop a nonlinear EMEH model and validate it experimentally, achieving strong agreement with the prototype (R² = 0.95 for RMS EMF). Using this model, we perform a parametric analysis of excitation frequency and the spacing between the fixed magnets (d), yielding practical design criteria for geometry selection. The validated model predicts a narrow maximum; for the present configuration and parameter bounds, it occurs at d ≈ 28 mm with P_out ≈ 151.94 mW, and the corresponding energy density is ρ_E ≈ 9.84 mW cm⁻³. These results yield a practical design rule for selecting d given target metrics and dimensional constraints, providing guidance for the design of compact, low-frequency harvesters powering autonomous sensor nodes. Full article

Physical Unclonable Functions (PUFs) are hardware-based security primitives that can produce unique digital identifiers from electronic devices. They are particularly useful for Internet of Things (IoT) applications due to their low cost and ability to improve security on lightweight devices. In this paper, we propose a new lightweight delay-based Linear Feedback Shift Register (LFSR) PUF with configurable primitive feedback. Our configurable PUF offers various important benefits, such as a compact architecture, low hardware overhead, a large challenge-response space, conservative power requirements, and flexibility to operate in different modes. We implement our proposed PUF on an FPGA, and the experimental results demonstrate that our PUF exhibits nearly ideal performance metrics in terms of uniformity and uniqueness, with minimal hardware overhead and low power consumption. Moreover, our PUF also passes the National Institute of Standards and Technology (NIST) statistical test suite. We also show that our proposed PUF is resistant to Machine Learning (ML) attacks. Full article

Let $(X_i,d_i)$ be a compact metric space with metric $d_i, i=1,2\dots ,k$, and G be a discrete infinitely countable amenable group. This paper is based on continuous actions $G\curvearrowright X_i$ on compact metric spaces $(X_i,d_i)$. Firstly, we introduce the concept of weighted Bowen balls, and then use the concept of weighted Bowen balls to introduce the corresponding lower (upper) weighted local entropy, as well as propose the concept of weighted Bowen topological entropy defined in terms of Hausdorff dimension by weighted Bowen balls, and prove Billingsley-type theorem between these two types of entropies by using the equivalent definition of weighted Bowen topological entropy. Full article

To address the challenge of monitoring the postharvest jasmine bloom stages during industrial tea scenting processes, this study proposes an efficient U-shaped Network (U-Net) model with frequency–spatial cross-attention (FSCA-EUNet) to resolve critical bottlenecks, including repetitive backgrounds and small interclass differences, caused by stacked jasmine flowers during factory production. High-resolution images of stacked jasmine flowers were first preprocessed and input into FSCA-EUNet, where the encoder extracted multi-scale spatial features and the FSCA module incorporated frequency-domain textures. The decoder then fused and refined these features, and the final classification layer output the predicted bloom stage for each image. The proposed model was designed as a “U-Net”-like structure to preserve multiscale details and employed a frequency–spatial cross-attention module to extract high-frequency texture features via a discrete cosine transform. Long-range dependencies were established by NonLocalBlook, located after the encoders in the model. Finally, a momentum-updated center loss function was introduced to constrain the feature space distribution and enhance intraclass compactness. According to the experimental results, the proposed model achieved the best metrics, including 95.52% precision, 95.42% recall, 95.40% F1-score, and 97.24% mean average precision, on our constructed dataset with only 878.851 K parameters and 15.445 G Floating Point Operations (FLOPs), and enabled real-time deployment at 22.33 FPS on Jetson Orin NX edge devices. The ablation experiments validated the improvements contributed by each module, which significantly improved the fine-grained classification capability of the proposed network. In conclusion, FSCA-EUNet effectively addresses the challenges of stacked flower backgrounds and subtle interclass differences, offering a lightweight yet accurate framework that enables real-time deployment for industrial jasmine tea scenting automation. Full article

Background/Objectives: Cancer is a chronic and heterogeneous disease, possessing molecular variation within a single type, resulting in its molecular subtypes. Cancer molecular subtyping offers biological insights into cancer variability, facilitating the development of personalized medicines. Various models have been proposed for cancer molecular subtyping, utilizing the high-dimensional transcriptomic, genomic, or proteomic data. The issue of data scarcity, characterized by high feature dimensionality and a limited sample size, remains a persistent problem.The objective of this research is to propose a deep learning framework, DeepCMS, that leverages the capabilities of feed-forward neural networks, gene set enrichment analysis, and feature selection to construct a well-representative subset of the feature space, thereby producing promising results. Methods: The gene expression data were transformed into enrichment scores, resulting in over 22,000 features. From those, the top 2000 features were selected, and deep learning was applied to these features. The encouraging outcomes indicate the efficacy of the proposed framework in terms of defining a well-representative feature space and accurately classifying cancer molecular subtypes. Results: DeepCMS consistently outperformed state-of-the-art models in aggregated accuracy, sensitivity, specificity, and balanced accuracy. The aggregated metrics surpassed 0.90 for all efficiency measures on independent test datasets, showing the generalizability and robustness of our framework. Although developed using colon cancer’s gene expression data, this approach may be applied to any gene expression data; a case study is also devised for illustration. Conclusions: Overall, the proposed DeepCMS framework enables the accurate and robust classification of cancer molecular subtypes using a compact and informative feature set, facilitating improved precision in oncology applications. Full article