Unified Spectrospatial Forward Models: Spatially Continuous Maps of Weak Emission Lines in the Rosette Nebula with SDSS-V LVM

Surface roughness is a critical quality attribute in laser cutting, directly influencing edge integrity, dimensional accuracy, and post-processing requirements. While most studies address surface roughness through forward modeling and optimization, practical manufacturing tasks often require solving inverse parameter selection problems, where process parameters must be chosen to satisfy prescribed surface quality requirements. In this study, surface roughness control in laser cutting is formulated within an inverse target-tracking framework based on response surface methodology (RSM). A quadratic response surface model is established using a Box–Behnken experimental design, with cutting speed, laser power, and assist-gas pressure as input factors. The fitted response surface provides an explicit forward mapping within a bounded operating window and serves as a local surrogate for methodological demonstration of target-oriented parameter estimation. Based on this surrogate model, a model-predicted feasible roughness range within the investigated design space is identified as Ra = 1.952–4.212 μm. For prescribed roughness targets within this interval, an inverse least-squares target-tracking formulation is employed to compute model-based parameter estimates. The inverse results are presented as continuous set-point maps and tabulated operating conditions, accompanied by a target-versus-predicted consistency check performed at the model level. Owing to the statistically significant lack-of-fit of the forward response surface, the inverse results presented in this study should be interpreted as theoretical, model-based estimates intended to illustrate the proposed framework rather than as experimentally validated process set-points. The proposed approach highlights both the potential and the limitations of inverse target-tracking strategies based on response surface models and underscores the need for statistically adequate models and independent experimental validation for industrial application.

The widespread adoption of electric vehicles (EVs) has posed significant challenges to the security of distribution grid loads. To address issues such as increased grid load fluctuations, rising user charging costs, and rapid load surges around midnight caused by uncoordinated nighttime charging of household electric vehicles in communities, this paper first models electric vehicle charging behavior as a Markov Decision Process (MDP). By improving the state-space sampling mechanism, a continuous space mapping and a priority mechanism are designed to transform the charging scheduling problem into a continuous decision-making framework while optimizing the dynamic adjustment between state and action spaces. On this basis, to achieve synergistic load forecasting and charging scheduling decisions, a forecast-augmented deep reinforcement learning method integrating Gated Recurrent Unit and Twin Delayed Deep Deterministic Policy Gradient (GRU-TD3) is proposed. This method constructs a multi-objective reward function that comprehensively considers time-of-use electricity pricing, load stability, and user demands. The method also applies a single-objective pre-training phase and a model-specific importance-sampling strategy to improve learning efficiency and policy stability. Its effectiveness is verified through extensive comparative and ablation validation. The results show that our method outperforms several benchmarks. Specifically, compared to the Deep Deterministic Policy Gradient (DDPG) and Particle Swarm Optimization (PSO) algorithms, it reduces user costs by 11.7% and the load standard deviation by 12.9%. In contrast to uncoordinated charging strategies, it achieves a 42.5% reduction in user costs and a 20.3% decrease in load standard deviation. Moreover, relative to single-objective cost optimization approaches, the proposed algorithm effectively suppresses short-term load growth rates and mitigates the “midnight peak” phenomenon.

The High Mountain Asia (HMA) region has the highest concentrations of high-altitude lakes in the world and experienced more frequent glacial lake outburst floods (GLOFs) in recent decades. Continuous monitoring and mapping of glacial lakes at high spatiotemporal resolution are crucial for understanding this rapidly evolving and vast landscape as well as associated disasters. While existing automated methods show significant promise for mapping glacial lakes, their completeness and accuracy need further improvement to regularly produce glacial lake databases in highly dynamic regions like HMA. In this study, we present a fully automated method integrating open-source remote sensing datasets, including Landsat-8, Sentinel-1, Sentinel-2, and Copernicus Digital Elevation Model (DEM), to map glacial lakes and generate a comprehensive inventory of glacial lakes across the HMA region. Our 2022 inventory comprising 31,698 glacial lakes across HMA covers an area of approximately 2,240 km[Formula: see text]. Most lakes are situated between 4000-5400 m asl elevations, with the Eastern Himalaya exhibiting the greatest lake area coverage. We achieved robust accuracy exceeding 96% in the glacial lake size bin (20,000-100,000 m[Formula: see text]), demonstrating the effectiveness of our method in mapping and detecting small lakes while successfully delineating all larger glacial lakes (> 100,000 m[Formula: see text]). The method was applied to two observation periods (2016-17 and 2022-24), enabling analysis of changes in lake area and spatial distribution patterns. Across HMA subregions, Qilian Shan region showed the highest expansion rate of 22.5% between the observation periods, while the Pamir region showed the least changes (2.9%) in this period, contributing to a 5.5% net change in overall glacial lake area at the HMA scale. Our automated approach provides substantial improvements over previous methodologies in data integration, accuracy and completeness, which can be utilized for routine updating of glacial lakes in HMA and elsewhere.

We prove a generalization of the topological Tverberg theorem. One special instance of our general theorem is the following: Let Δ \Delta denote the 8-dimensional simplex viewed as an abstract simplicial complex, and suppose that its vertices are arranged in a 3 × 3 3\times 3 array. Then for any continuous map f : Δ → R 3 f:\Delta \to \mathbb {R}^3 it is possible to partition the rows or the columns of the vertex array into two parts, such that the disjoint faces σ \sigma and τ \tau induced by the two parts satisfy f ( σ ) ∩ f ( τ ) ≠ ∅ f(\sigma )\cap f(\tau ) \neq \emptyset . Our result also has consequences for geometric transversals and topological Helly theorems.

Abstract. In the hyper-arid Namib Desert, fog serves as the only regular source of moisture, vital for sustaining local ecosystems. While fog occurrence in the region is typically associated with the advection of marine stratus clouds and their interaction with topography, its spatial distribution is strongly influenced by cloud base height, which remains poorly understood. To address this gap, this study utilizes ground-based remote sensing and in-situ observations to analyze systematic spatial and temporal patterns of cloud base height. Our results reveal clear seasonality and a diurnal cycle, with cloud base lowering moderately (10–50 m h−1) during the evening and early night, and lifting rapidly (30–150 m h−1) after sunrise, especially inland. Additionally, the findings indicate that these rates are influenced by horizontal gradients in cloud thickness. Quantile regression highlights the tight relationship between cloud base height and near-surface relative humidity (r≈-0.76) that is expected in well-mixed boundary layer, which can therefore be employed to estimate cloud base height across FogNet sites. In a case study, the potential value of the estimated cloud base height for separating fog from low clouds in satellite-based products is shown. In the future, a full integration of the estimated cloud base height with a satellite-based fog and low-cloud product can enable a spatially continuous mapping of fog in the region for the first time, which would facilitate fog ecological impact studies.

The investigation of chaos is an important field of science and has got many significant achievements. In the earlier age of the field, the main focus is on the study of the systems that are smooth everywhere. Less attention has been paid to nonsmooth systems. Nonsmooth dynamical systems are broadly appeared in practices, such as impact oscillators, relaxation oscillators, switch circuits, neuron firing, epidemic and even economic models, and have become an active field of study recently. The typical characteristics of those systems is the abruptly variation of the dynamics after slowly evolving over a longer time. Piecewise smooth maps are a type of important models and often employed to describe the dynamics of those systems. Among them, much attention is paid to a class of generally one dimensional piecewise linear discontinuous maps since they are easy to hand and can display rich classes of dynamical phenomena with new characteristics.<br>Enclosed in this work is a discontinuous two-piece mapping function. The left branch is a linear function with slope $\alpha$, and the right is a power law function with exponent $z$. There is a gap confined by $[\mu,\mu+\delta]$ at $x=0$, where $\mu$ is the control parameter, and $\delta$ is the with of the gap. Even though the dynamics of nonsmooth and continuous maps under some special $z$ values have been intensively studied, while their discontinuous counterparts have not been investigated under arbitrary $z$ and discontinuous gap $\delta$. The appearance of the discontinuity may induce border collision bifurcations. The interplay between the bifurcations associated with stability analysis and the border collision bifurcations may produce complex dynamics with new characteristics. Therefore, the investigation on the dynamics of those maps are carried out in this paper, in which the periodic increments, periodic adding and coexistence of attractors are observed. The border collision bifurcation often interrupts a stable periodic orbit and make it transform to a chaotic state or another periodic orbit. In the neighborhood of critical parameters of this bifurcation, there often occurs the coexistence of a periodic orbit with a chaotical or another periodic attractor. A general approach is proposed to analytically and numerically calculate the critical control parameters at which the border collision bifurcations happen, which transform the problem into the solution of an algebraic equation of dimensionless control parameter $\mu/\mu_0$, where $\mu_0$ is the critical control parameter when $\delta=0$. The solution can be obtained analytically when $z$ is a simple rational number or small integer, and numerically for an arbitrary real number. By this way, the stability condition and critical control parameters for the periodic orbit of type $L^{n-1}R$ are analytically or numerically obtained under the arbitrary exponent $z$ and discontinuous gap $\delta$. The results are accordance with the numerical simulations very well. Based on the stability and border collision bifurcation analysis, the phase diagrams in the plane of two dimensional parameters $\mu-\delta$ are built for different ranges of $z$. Their dynamical behaviors are discussed, and three types of co-dimension-2 bifurcations are observed, and the general expressions for the coordinates at which those phenomena occur are obtained in the phase plane. Meanwhile, a specular tripe-point induced by merging of co-dimension-2 bifurcation points $\mathrm{BC-flip}$ and $\mathrm{BC-BC}$ is observed in the phase plane, and the condition for the appearance of it is analytical obtained.

Background: Constant pressure on certain body regions can cause bedsores, also called pressure ulcers, which are lesions to the skin or soft tissues that can have fatal implications if left untreated. This study highlights areas where nurses' competencies are lacking. It demonstrates how evidence-based interventions, targeted education, and institutional support can effectively reduce the prevalence of pressure ulcers and enhance patient safety in intensive care units. Purpose: The purpose of this review is to summarize and critically evaluate the body of research on ICU nurses' knowledge, attitude, and practice regarding pressure ulcer prevention. Methods: This review analyzed pressure ulcer prevention studies among ICU nurses using keywords like “prevalence, incidence, risk factors, complications, knowledge, attitude, and practice”. Relevant peer-reviewed articles were retrieved from multiple databases, including PubMed (via Medline), ScienceDirect, Google Scholar, ResearchGate, and the Cochrane Library. Methodological quality was ensured to maintain reliability and validity. The articles were retrieved from the period between 2015 and 2025. Results: The study identified 515 articles, screened 477, and selected 19 for inclusion in a narrative review. The studies examined nurses' knowledge, attitude, and practice regarding pressure ulcer prevention in intensive care settings. Conclusion: Nurses play a critical role in preventing pressure ulcers, and educating them about risk assessment and prevention can improve patient outcomes. Best practices include routine skin exams, systematic risk assessments, care planning, continuous pressure mapping, and the use of prophylactic dressings. Implications for Nursing: The review highlights the importance of ongoing education and competency-based training in nursing practice for preventing pressure ulcers in ICUs. It suggests integrating standardized guidelines, ensuring adequate staffing, and fostering accountability roles, can advocate for improved water management policies that prioritize health outcomes. Keywords: Nurses’ knowledge, Intensive care, Pressure ulcer prevention, Jordan.

Introduction. The relevance of the cartographic method in toponymy is justified by the spatial nature of the naming process itself, which is realized within discrete geographical objects. Despite this, in studies devoted to local toponymic systems, cartographic analysis is used only sporadically. The aim of this research is to demonstrate the effectiveness of comprehensive microtoponym mapping for solving both purely toponymic tasks and broader tasks of an ethnocultural nature. Materials and Methods. The research material was the Card Index of Karelia Toponyms, in which a significant portion of the microtoponyms are linked to topographic maps. Based on the card index data, an electronic resource – the “Toponymy of Karelia” geographic information system (GIS) – was created, which enables the mapping of toponymy within local topo-systems. The study employs maps of various formats as illustrations, ranging from standard maps of the “Atlas of Karelia” (scale 1 cm = 1 km) to field sketches and electronic maps in the OpenStreetMap format. In addition to the cartographic method itself, the methodology of etymological reconstruction and semantic analysis was employed. Results and Discussion. This article examines three applications of the method of comprehensive microtoponym mapping. Its contribution to solving core toponymic tasks (problems of nomination) is illustrated by the route-based perspective that mapping reveals. The potential of comprehensive microtoponymic mapping for extracting ethnocultural information is also demonstrated. Through the areal distribution of microtoponyms with Russian and Karelian-derived stems, the primary routes of Russian linguistic influence into the specific local territory of the historical Vyrozero Volost in Zaonezhye are outlined. Localization is often a decisive factor in determining toponymic origin. The article demonstrates its use in establishing the Sami roots of two island toponyms (Oryatsaari and Pellotsaari), which encapsulate the idea of the islands’ position relative to the center of an island archipelago in the Ladoga region. A geographical motivation is proposed for the toponymic stem Akka- (Gen. Akan-) meaning ‘old woman’ or ‘crone’, prompted by a linguistic metaphor. Conclusion. The method of continuous mapping of local topo-systems allows for a more in-depth understanding of the nature of toponymic nomination and also facilitates the identification of etymological, cultural-historical, and other information embedded in the localization of toponyms. In this regard, the experience of the approaches outlined in the article is useful for application in other toponymic expeditions. The research results contribute to the development of the cartographic method, as well as to the study of toponymic nomination within a local toponymic system.

The challenges of high computational complexity as well as the corresponding long time consumption are like the Achilles’ Heel in the traditional numerical methods for solving the large-scale underwater acoustic field. An efficient solution method for the parabolic equation model based on the Fourier Neural Operator was proposed in this work. This method enables efficient global feature extraction through spectral convolution, thereby effectively establishing robust correlations between physical field parameters and the target sound pressure field. A continuous mapping was constructed in this model, which ensures that this algorithm could effectively adapt to various marine scenarios through the self-adjustment function. Experimental results demonstrate that the model achieves an average coefficient of determination R 2 > 0.95 and a relative Root Mean Square Error (RMSE) < 0.04 dB in the predicted sound pressure field, which represents various complex ocean conditions, including the scenarios with non-uniform sound speed profiles, broadband sound sources, and sloped bathymetry, among others. Compared to the conventional RAM approach, the model proposed in this study achieves the equivalent accuracy while reducing the computational latency, with a demonstrated decrease ranging from 25% to 35%. This superior performance could be attributed to the adopted grid-independent O ( nlogn ) spectral convolution architecture. These results demonstrate the robustness and applicability of the framework, highlighting the potential for broader application in underwater sound field prediction in the future.

We study the diagonals g(x)=f(x,...,x) of strongly separately continuous mappings f:Xn→Z, that is, mappings which for a fixed value of one variable are jointly continuous with respect to the others variables. We prove that for any n≥2, any topological space X, any strongly σ-metrizable equiconnected space (Z,λ) with a perfect stratification assigned with a mapping λ and every Baire class one mapping g:X→ℝ there exists a strongly separately continuous mapping f:Xn→Z with the diagonal g. From this we obtain that for any PP-space space X and any strongly σ-metrizable equiconnected space (Z,λ) with a perfect stratification assigned with a mapping λ the diagonals of strongly separately continuous mappings f:Xn→Z are exactly Baire class one mappings. Moreover, we prove that for a countably compact space X the diagonals of strongly separately continuous functions f:Xn→ℝ coincide with the functions of Baire class one if and only if every system of functionally open pairwise disjoint sets in X is at most countable.

Piecewise parametric surfaces have long been established as prevalent geometric representations; however, they often require surface refinement or sophisticated quadrangulation to accurately represent complex geometries. Geometric deep learning has shown that neural networks can provide greater representational power than conventional methods. Nevertheless, approaches using a single parametric surface for shape fitting struggle to capture fine-grained geometric details, while multi-patch methods fail to ensure seamless connections between adjacent patches. We present Neural Piecewise Parametric Surfaces ( NeuPPS ), the first piecewise neural surface representation that allows for coarse patch layouts composed of arbitrary n -sided surface patches to model complex surface geometries with high precision, offering enhanced flexibility compared with traditional parametric surfaces. This new surface representation guarantees, by construction, the continuity between adjacent patches, a property that other neural patch-based approaches cannot ensure. Two novel components are introduced: a learnable feature complex and a continuous mapping function approximated by multi-layer perceptrons (MLPs). We apply the proposed NeuPPS to surface fitting and shape space learning tasks. Extensive experiments demonstrate the advantages of NeuPPS over traditional parametric representations and existing patch-based learning approaches.

We construct a continuous map from the space of orders on quandles to the space of quandle actions on one-manifolds, providing an answer to a question posed by Idrissa Ba and Mohamed Elhamdadi. As an application of this map, we characterize isolated orders on quandles in terms of strong rigidity. As another application, we prove that there is no isolated right order on the free quandles, except for specific cases.

Research on microplastics (MPs) in agricultural soils has received increasing attention due to their potential ecological risks and adverse effects on the food chain. Recently, geostatistical approaches have been increasingly used to assess the spatial distribution of MPs in soils. Therefore, this study aims to predict the abundance of MPs in the soil of an agricultural micro-watershed using geostatistical methods and to produce a continuous map of the interpolated MPs. Soil samples were collected, and MP abundance was determined using the density separation method. Subsequently, exploratory data analysis was conducted, followed by the construction of the experimental semivariogram, theoretical variogram model fitting, ordinary kriging interpolation, cross-validation and, inverse distance weighting (IDW) interpolation. MPs were detected in all samples, with average abundances of 3826, 2553, and 3407 pieces kg−1 in forest, pasture, and agricultural land use systems, respectively. The experimental semivariogram showed that the spatial distribution of MPs has a weak spatial dependence structure. The Kriging and IDW maps showed a distribution of MPs in the range of 600 to 7400 pieces kg−1, with higher concentrations of MPs for forest and agricultural areas. Additionally, the map reveals a high abundance of MPs, with greater concentrations in depressions and areas near roads and urban centers, allowing for identifying critical points within the micro-watershed. This study offers important insights into the presence of MPs across various land uses, emphasizing the need for proactive measures to prevent and mitigate their accumulation in soil.

We introduce the concept of F-decomposable systems, well-ordered inverse systems of Hausdorff compacta with fully closed bonding mappings. A continuous mapping between Hausdorff compacta is called fully closed if the intersection of the images of any two closed disjoint subsets is finite. We give a characterization of such systems in terms of a property of the continuous functions on their limit. When, moreover, the fibers of neighboring bonding mappings are metrizable, we call the limit of such a system an F d \mathrm {F}_d -compact, a particular case of a Fedorchuk compact. The stated property allows us to obtain a locally uniformly rotund renorming on the space C ( K ) C(K) , where K K is an F d \mathrm {F}_d -compact of countable spectral height.

ABSTRACT Metasurfaces provide powerful control over the amplitude, phase, polarization, and wavelength of light, enabling compact and multifunctional photonic systems. However, designing metasurfaces with high‐dimensional multiplexing capabilities often requires composite or interleaved meta‐atom configurations, which can introduce fabrication complexity, near‐field coupling, and limited scalability. Here, we present an end‐to‐end differentiable design framework that integrates meta‐atom geometry modeling with global optical performance optimization. By leveraging a neural network–based surrogate model, we establish a continuous mapping between geometric parameters and polarization‐dependent optical responses, allowing gradient‐based co‐optimization of metasurface functionality using only single‐type, fabrication‐friendly meta‐atoms. We experimentally demonstrate a single‐layer metasurface that achieves eight‐channel polarization multiplexing at a single operating wavelength, simultaneously generating distinct nanoprinting patterns and 3D holograms with minimal inter‐channel crosstalk. Extending this approach across two wavelengths enables 16 independent optical channels, validating the scalability of the framework. The proposed strategy unifies structural simplicity with functional versatility, offering a robust and generalizable platform for advanced applications in high‐capacity optical displays, secure data encoding, and integrated photonic systems.

A novel optimization method for transducer array in Lamb wave detection of variable cross-section structures.

From urban to nature: A continuous landscape gradient mapping framework in Southwest China.

Self-calibrating multiplexed microneedle electrode array for continuous mapping of subcutaneous multi-analytes in diabetes

We introduce and explore Lξ-families, an innovative class of localized topological structures that extends classical concepts while preserving fundamental properties. These families constitute a bridge between traditional topological objects and finer-grained local-to-global characteristics. Our construction offers a natural generalization of regular open sets through a novel localization approach that maintains critical topological invariants across various transformations and operations. This paper establishes the foundational theory of Lξ-families, proving key characterization theorems and situating them within the broader topological landscape. Our findings reveal that these structures form a complete lattice under appropriate operations and possess significant hereditary characteristics. Additionally, we demonstrate stability properties under continuous mappings and homeomorphisms, highlighting their seamless integration with established topological frameworks. Through strategically selected counterexamples, we define the boundaries of these new concepts. The theoretical architecture developed in this work creates pathways for applications in digital topology and image processing, with particularly promising implications for edge detection and boundary analysis methods. The relationships we establish between Lξ family members and classical topological concepts provide unifying perspectives across seemingly disparate notions and introduce novel tools for topological classification challenges.