Dimensions Research Articles

Analytical prediction of the formation factor for anisotropic mono-sized unconsolidated porous media

The rectangular Representative Unit Cell (RUC) models for mono-sized isotropic unconsolidated porous media have been extended to anisotropic media. Volume averaging was applied to Ohm's law in order to propose analytical expressions for the formation factor for electrical conduction in terms of the pore-scale linear dimensions. The formation factor, crucial for understanding electrical conduction in porous media, has significant applications in subsurface geophysics, petroleum reservoir characterization, and the durability assessment of construction materials. These analytical models provide valuable insights for optimizing the electrical properties of porous structures in various engineering fields, for example in mapping groundwater resources, differentiating oil-bearing zones in reservoirs, and predicting ion migration in concrete. Aspect ratios of the cell and solid dimensions have been introduced, and the formation factor expressed in terms thereof for five different arrays, i.e. a regular, a non-overlapping streamwisely fully staggered, an overlapping streamwisely fully staggered, a non-overlapping transversally fully staggered, and an overlapping transversally fully staggered array. The Laplace equation has furthermore been solved numerically for two-dimensional versions of the different arrays and the formation factor computed for several values of the aspect ratios. The proposed analytical models have been validated against the generated numerical data and compared to experimental and numerical data obtained from the literature. The proposed models have also been adapted to include a percolation threshold porosity in order to improve the model predictions for very low porosity media.

Domain knowledge-enhanced multi-spatial multi-temporal [formula omitted] forecasting with integrated monitoring and reanalysis data

Accurate air quality forecasting is crucial for public health, environmental monitoring and protection, and urban planning. However, existing methods fail to effectively utilize multi-scale information, both spatially and temporally. There is a lack of integration between individual monitoring stations and city-wide scales. Temporally, the periodic nature of air quality variations is often overlooked or inadequately considered. To overcome these limitations, we conduct a thorough analysis of the data and tasks, integrating spatio-temporal multi-scale domain knowledge. We present a novel Multi-spatial Multi-temporal air quality forecasting method based on Graph Convolutional Networks and Gated Recurrent Units (M2G2), bridging the gap in air quality forecasting across spatial and temporal scales. The proposed framework consists of two modules: Multi-scale Spatial GCN (MS-GCN) for spatial information fusion and Multi-scale Temporal GRU (MT-GRU) for temporal information integration. In the spatial dimension, the MS-GCN module employs a bidirectional learnable structure and a residual structure, enabling comprehensive information exchange between individual monitoring stations and the city-scale graph. Regarding the temporal dimension, the MT-GRU module adaptively combines information from different temporal scales through parallel hidden states. Leveraging meteorological indicators and four air quality indicators, we present comprehensive comparative analyses and ablation experiments, showcasing the higher accuracy of M2G2 in comparison to nine currently available advanced approaches across all aspects. The improvements of M2G2 over the second-best method on RMSE of 72-h future predictions are as follows: PM2.5: 6%∼10%; PM10: 5%∼7%; NO2: 5%∼16%; O3: 6%∼9%. Furthermore, we demonstrate the effectiveness of each module of M2G2 by ablation study. We conduct a sensitivity analysis of air quality and meteorological data, finding that the introduction of O3 adversely impacts the prediction accuracy of PM2.5.

Different coexistence patterns between apex carnivores and mesocarnivores based on temporal, spatial, and dietary niche partitioning analysis in Qilian Mountain National Park, China.

Carnivores play key roles in maintaining ecosystem structure and function as well as ecological processes. Understanding how sympatric species coexist in natural ecosystems is a central research topic in community ecology and biodiversity conservation. In this study, we explored intra- and interspecific niche partitioning along spatial, temporal, and dietary niche partitioning between apex carnivores (wolf Canis lupus, snow leopard Panthera uncia, Eurasian lynx Lynx lynx) and mesocarnivores (Pallas's cat Otocolobus manul, red fox Vulpes vulpes, Tibetan fox Vulpes ferrilata) in Qilian Mountain National Park, China, using camera trapping data and DNA metabarcoding sequencing data. Our study showed that apex carnivore species had more overlap temporally (coefficients of interspecific overlap ranging from 0.661 to 0.900) or trophically (Pianka's index ranging from 0.458 to 0.892), mesocarnivore species had high dietary overlap with each other (Pianka's index ranging from 0.945 to 0.997), and apex carnivore and mesocarnivore species had high temporal overlap (coefficients of interspecific overlap ranging from 0.497 to 0.855). Large dietary overlap was observed between wolf and snow leopard (Pianka's index = 0.892) and Pallas's cat and Tibetan fox (Pianka's index = 0.997), suggesting the potential for increased resource competition for these species pairs. We concluded that spatial niche partitioning is likely to key driver in facilitating the coexistence of apex carnivore species, while spatial and temporal niche partitioning likely facilitate the coexistence of mesocarnivore species, and spatial and dietary niche partitioning facilitate the coexistence between apex and mesocarnivore species. Our findings consider partitioning across temporal, spatial, and dietary dimensions while examining diverse coexistence patterns of carnivore species in Qilian Mountain National Park, China. These findings will contribute substantially to current understanding of carnivore guilds and effective conservation management in fragile alpine ecosystems.

2D Embeddings of Multi-dimensional Partitionings.

Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models, where each segment of the partitioning represents a region of similar model behavior. Having computed a partitioning, one is commonly interested in understanding how large the segments are and which segments lie next to each other. While visual representations of 2D domain partitionings that reveal sizes and neighborhoods are straightforward, this is no longer the case when considering multi-dimensional domains of three or more dimensions. We propose an algorithm for computing 2D embeddings of multi-dimensional partitionings. The embedding shall have the following properties: It shall maintain the topology of the partitioning and optimize the area sizes and joint boundary lengths of the embedded segments to match the respective sizes and lengths in the multi-dimensional domain. We demonstrate the effectiveness of our approach by applying it to different use cases, including the visual exploration of 3D spatial domain segmentations and multi-dimensional parameter space partitionings of simulation ensembles. We numerically evaluate our algorithm with respect to how well sizes and lengths are preserved depending on the dimensionality of the domain and the number of segments.

Parallelization of particle-mass-transfer algorithms on shared-memory, multi-core CPUs

Simulating the transfer of mass between particles is not straightforwardly parallelized because it involves the calculation of the influence of many particles on each other. Engdahl et al. (2019) intuited that the number of matrix operations used for mass transfer grows quadratically with the number of particles, so that dividing the domain geometrically into sub-domains will give speed and memory advantages, even on a single processing thread. Those authors also showed the speed scalability of several one-dimensional examples on multiple cores. Here, we extend those results for more general cases, both in terms of spatial dimensions and algorithmic implementation. We show that there is an optimal subdivision scheme for naive, full-matrix calculations on a multi-processor, or multi-threading shared-memory machine. A similar sparse-matrix implementation that also uses row-and-column-sum normalization often greatly reduces the memory requirements. We also introduce a completely new mass transfer algorithm that uses a non-geometric domain decomposition and only matrix row-sum normalization. This allows the mass-transfer “matrix” to be constructed and solved one row at a time in parallel, so it is faster and vastly more memory efficient than previous methods, but requires more care for suitable accuracy.

Can ecological zoning act as an environmental management tool for protecting regional habitat quality: Causal evidence from the national key ecological function zone in China

Habitat degradation is one of the most serious environmental problems worldwide, which threatens human wellbeing and sustainable development. Exploring how to protect natural habitats has become a research hotspot in the environmental management field. Ecological zoning has been widely used in habitat protection, but its actual effectiveness has been rarely revealed, especially with the robust and reliable causal inference method. Therefore, taking the Yangtze River Economic Belt (YREB) in China as the study area, we first quantified habitat quality and changes at the district/county scale during 2005–2019. Then, we used the National Key Ecological Function Zone (NKEFZ) as a representative ecological zone scheme, and explored the effectiveness of the NKEFZ in protecting habitat quality with the Propensity Score Matching and Difference-in-Difference combined method, which is a representative causal inference method. We found that habitat quality showed an uneven distribution during the study period, and habitat quality of districts/counties within the NKEFZ was higher than that outside the NKEFZ with statistical significance. Most districts/counties experienced a habitat quality decrease, but the decrease within the NKEFZ is less than that outside the NKEFZ. We observed that the NKEFZ can protect habitat quality from the causal relationship perspective, but there was the spatio-temporal heterogeneity of the NKEFZ effectiveness. In terms of the spatial dimension, the NKEFZ was the most effective in the Lower Reach of the YREB. In terms of the temporal dimension, there was a 1-year time-lag effect of the NKEFZ effectiveness, and NKEFZ effectiveness experienced a sharp increase from 2016. The NKEFZ contributed to protecting habitat quality through multiple management strategies such as urban land quota, high pollution industry prohibition, and ecological compensation. Overall, this study verified that the ecological zone scheme can contribute to habitat quality protection, and emphasizes that the effectiveness of ecological zoning may vary across time and space. This work can support ecological zoning implementation with robust evidence, and provides a novel perspective for understanding the effectiveness of ecological zoning.

Multi-Step Passenger Flow Prediction for Urban Metro System Based on Spatial-Temporal Graph Neural Network

Efficient operation of urban metro systems depends on accurate passenger flow predictions, a task complicated by intricate spatiotemporal correlations. This paper introduces a novel spatiotemporal graph neural network (STGNN) designed explicitly for predicting multistep passenger flow within metro stations. In the spatial dimension, previous research primarily focuses on local spatial dependencies, struggling to capture implicit global information. We propose a spatial modeling module that leverages a dynamic global attention network (DGAN) to capture dynamic global information from all-pair interactions, intricately fusing prior knowledge from the input graph with a graph convolutional network. In the temporal dimension, we design a temporal modeling module tailored to navigate the challenges of both long-term and recent-term temporal passenger flow patterns. This module consists of series decomposition blocks and locality-aware sparse attention (LSA) blocks to incorporate multiple local contexts and reduce computational complexities in long sequence modeling. Experiments conducted on both simulated and real-world datasets validate the exceptional predictive performance of our proposed model.

A spatiotemporal comparative analysis on tumor immune microenvironment characteristics between neoadjuvant chemotherapy and preoperative immunotherapy for ESCC

The average five-year survival rate for esophageal cancer, a common malignant tumor of the digestive system, is barely 20%. The majority of esophageal squamous cell carcinoma (ESCC) patients had already progressed to a locally advanced or even advanced stage at initial diagnosis, making routine surgery ineffective. Chemotherapy and immunotherapy are important neoadjuvant treatments for ESCC, however, it remains unknown how treatment will affect the immunological microenvironment, especially at the spatial level. Here, we presented the TME characters of ESCC from the temporal and spatial dimensions using scRNA-seq and ST, investigated the changes of immune cell clusters in the TME under neoadjuvant chemotherapy and preoperative immunotherapy, and explored the potential mechanisms. It was found that compared with chemotherapy, immunotherapy combined with chemotherapy increased the level of T cell proliferation, partially restored the function of exhausted T cells, induced the expansion of specific exhausted CD8 T cells, increased the production of dendritic cells (DCs), and supported the immune hot microenvironment of the tumor. We also found that CD52 and ID3 have potential as biomarkers of ESCC. Particularly, CD52 may be served as a predictor of the efficacy to screen the advantaged population of different regimens. Through multiple pathways, CAF2 and CAF5’s antigen-presenting role affected the other fibroblast clusters, resulting in malignant transformation. We analyzed the immune microenvironment differences between the two regimens to provide a more thorough description of the ESCC microenvironment profile and serve as a foundation for customized neoadjuvant treatment of ESCC.

Equilibrium measures for two-sided shift spaces via dimension theory

Abstract Given a two-sided shift space on a finite alphabet and a continuous potential function, we give conditions under which an equilibrium measure can be described using a construction analogous to Hausdorff measure that goes back to the work of Bowen. This construction was previously applied to smooth uniformly and partially hyperbolic systems by the first author, Pesin, and Zelerowicz. Our results here apply to all subshifts of finite type and Hölder continuous potentials, but extend beyond this setting, and we also apply them to shift spaces with synchronizing words.

Top-k sentiment analysis over spatio-temporal data.

In recent years, social media has become much more popular to use to express people's feelings in different forms. Social media such as X (i.e., Twitter) provides a huge amount of data to be analyzed by using sentiment analysis tools to examine the sentiment of people in an understandable way. Many works study sentiment analysis by taking in consideration the spatial and temporal dimensions to provide the most precise analysis of these data and to better understand people's opinions. But there is a need to facilitate and speed up the searching process to allow the user to find the sentiment analysis of recent top-k tweets in a specified location including the temporal aspect. This work comes with the aim of providing a general framework of data indexing and search query to simplify the search process and to get the results in an efficient way. The proposed query extends the fundamental spatial distance query, commonly used in spatial-temporal data analysis. This query, coupled with sentiment analysis, operates on an indexed dataset, classifying temporal data as positive, negative, or neutral. The proposed query demonstrates over a tenfold improvement in query time compared to the baseline index with various parameters such as top-k, query distance, and the number of query keywords.

A Deep Learning-Enhanced Compartmental Model and Its Application in Modeling Omicron in China.

The mainstream compartmental models require stochastic parameterization to estimate the transmission parameters between compartments, whose calculation depend upon detailed statistics on epidemiological characteristics, which are expensive, economically and resource-wise, to collect. In addition, infectious diseases spread in three dimensions: temporal, spatial, and mobile, i.e., they affect a population through not only the time progression of infection, but also the geographic distribution and physical mobility of the population. However, the parameterization process for the mainstream compartmental models does not effectively capture the spatial and mobile dimensions. As an alternative, deep learning techniques are utilized in estimating these stochastic parameters with greatly reduced dependency on data particularity and with a built-in temporal-spatial-mobile process that models the geographic distribution and physical mobility of the population. In particular, we apply DNN (Deep Neural Network) and LSTM (Long-Short Term Memory) techniques to estimate the transmission parameters in a customized compartmental model, then feed the estimated transmission parameters to the compartmental model to predict the development of the Omicron epidemic in China over the 28 days for the period between 4 June and 1 July 2022. The average levels of predication accuracy of the model are 98% and 92% for the number of infections and deaths, respectively. We establish that deep learning techniques provide an alternative to the prevalent compartmental modes and demonstrate the efficacy and potential of applying deep learning methodologies in predicting the dynamics of infectious diseases.

Mixed variational formulation and finite-element implementation of second-order poro-elasticity

We present a variational formulation of second-order poro-elasticity that can be readily implemented into finite-element codes by using standard Lagrangian interpolation functions. Point of departure is a two-field minimization principle in terms of the displacement and the fluid flux as independent variables. That principle is taken as a basis for the derivation of continuous and incremental saddle-point formulations in terms of an extended set of independent variables. By static condensation this formulation is then reduced to a minimization principle in terms of the displacement and fluid flux as well as associated higher-order fields. Once implemented into a finite-element code, the resulting formulation can be applied to the numerical simulation of porous media in consideration of second-order effects. Here, we analyze the model response by means of several example problems including two standard tests in poro-elasticity, namely the consolidation problems of Terzaghi and Mandel, and compare the results with those of a corresponding first-order model. As becomes clear, the second-order formulation can unleash its full potential when applied to the study of porous media having spatial dimensions comparable to the size of their microstructure. In particular, it is capable to regularize steep field gradients at external as well as internal surfaces and to describe material dilatation effects known from experiments.

The primacy model and the structure of olfactory space.

Understanding sensory processing relies on the establishment of a consistent relationship between the stimulus space, its neural representation, and perceptual quality. In olfaction, the difficulty in establishing these links lies partly in the complexity of the underlying odor input space and perceptual responses. Based on the recently proposed primacy model for concentration invariant odor identity representation and a few assumptions, we have developed a theoretical framework for mapping the odor input space to the response properties of olfactory receptors. We analyze a geometrical structure containing odor representations in a multidimensional space of receptor affinities and describe its low-dimensional implementation, the primacy hull. We propose the implications of the primacy hull for the structure of feedforward connectivity in early olfactory networks. We test the predictions of our theory by comparing the existing receptor-ligand affinity and connectivity data obtained in the fruit fly olfactory system. We find that the Kenyon cells of the insect mushroom body integrate inputs from the high-affinity (primacy) sets of olfactory receptors in agreement with the primacy theory.

Enhanced Parameter Estimation of DENsity CLUstEring (DENCLUE) Using Differential Evolution

The task of finding natural groupings within a dataset exploiting proximity of samples is known as clustering, an unsupervised learning approach. Density-based clustering algorithms, which identify arbitrarily shaped clusters using spatial dimensions and neighbourhood aspects, are sensitive to the selection of parameters. For instance, DENsity CLUstEring (DENCLUE)—a density-based clustering algorithm—requires a trial-and-error approach to find suitable parameters for optimal clusters. Earlier attempts to automate the parameter estimation of DENCLUE have been highly dependent either on the choice of prior data distribution (which could vary across datasets) or by fixing one parameter (which might not be optimal) and learning other parameters. This article addresses this challenge by learning the parameters of DENCLUE through the differential evolution optimisation technique without prior data distribution assumptions. Experimental evaluation of the proposed approach demonstrated consistent performance across datasets (synthetic and real datasets) containing clusters of arbitrary shapes. The clustering performance was evaluated using clustering validation metrics (e.g., Silhouette Score, Davies–Bouldin Index and Adjusted Rand Index) as well as qualitative visual analysis when compared with other density-based clustering algorithms, such as DPC, which is based on weighted local density sequences and nearest neighbour assignments (DPCSA) and Variable KDE-based DENCLUE (VDENCLUE).

Three-dimensional assessment on digital cast of spontaneous upper first molar distorotation after Ni-ti leaf springs expander and rapid maxillary expander: A two-centre randomized controlled trial.

The aim of this randomized controlled trial (RCT) was to evaluate the spontaneous distorotation of upper first permanent molars and the transverse dentoalveolar changes on digital casts in growing patients following maxillary expansion treatment using either the Leaf Expander® or the rapid maxillary expander (RME), both anchored to the deciduous second molar. This study was a two-arm, parallel-assignment, RCT with a dual-centre design conducted at two teaching hospitals in Italy. Inclusion criteria included maxillary transverse deficiency, prepubertal development stage (cervical vertebra maturation stage [CVMS] 1-2) and early mixed dentition with fully erupted upper first permanent molars. Exclusion criteria were systemic diseases or syndromes, CVMS 3-6, agenesis of upper second premolars, unavailability of the second deciduous molar for anchorage and Class III malocclusion. Patients were randomly assigned to the Leaf Expander® or RME group using a computer-generated randomization list created by a central randomization centre. Randomization was conducted immediately before the start of treatment. The intervention involved treatment with either the Leaf Expander® or the RME. Both devices were anchored to the second deciduous molars. Following randomization, patients were further categorized based on the presence of no crossbite, unilateral crossbite or bilateral crossbite. The primary outcome measure was the distorotation of the upper first molar (U6). Secondary outcomes included measurements of interdental linear dimensions, specifically upper inter-canine width (53-63), upper inter-molar width (MV16-MV26) and upper inter-deciduous second molar width (55-65). The examiner analysing the digital casts was blinded to the treatment groups to prevent detection bias and ensure objective assessment. However, due to the nature of the intervention, blinding was not feasible for the patients and clinicians involved in administering the treatment. A total of 150 patients were enrolled and randomly assigned to two groups: 75 to the Leaf Expander® group and 75 to the RME group. Recruitment started in November 2021 and was completed in November 2022. At the time of analysis, the trial was complete with no ongoing follow-ups. ANOVA tests revealed no significant differences between the three subgroups (no-cross, unilateral-cross and bilateral-cross) within both the Leaf Expander® and RME groups at T0. The Leaf Expander® demonstrated significantly greater distorotation in the unilateral crossbite subgroup compared to the RME (p = .014). In terms of total molar distorotation, the Leaf Expander® appliance showed a significantly greater effect (12.66°) compared with conventional RME (7.83°). Linear regression analysis demonstrated a significant correlation between the extent of expansion and the degree of molar rotation. Maxillary expansion resulted in significant spontaneous molar distorotation when the appliance was bonded to the second deciduous molars. The Leaf Expander® exhibited significantly greater molar distorotation compared with conventional RME. The degree of molar distorotation was correlated with the extent of expansion obtained on the second deciduous molar. The trial was registered at ClinicalTrials.gov (ID: NCT05135962).

Spatiotemporal Exploration of Ridesharing Services Ridership through Geovisualization: A Case Study of the New York City Region

App-based ridesharing services (RSSs), exemplified by platforms like Uber, play a pivotal role in modern transportation by offering convenient and on-demand services. The exploration of RSSs necessitates a comprehensive consideration of the inherent spatiotemporal variability within the data. Prior research, however, has tended to analyze the spatial and temporal dimensions separately, with many studies omitting the temporal aspect. This study addresses the gap by using geovisualization techniques to illustrate emerging hot spot analysis in New York City in 2022, derived from space–time data mining. Overall, despite temporal variations in overall RSSs ridership, certain taxi zones maintain distinct ridership patterns. Across the five New York City boroughs (Manhattan, Bronx, Queens, Brooklyn, and Staten Island), Midtown Manhattan and the Brooklyn areas adjacent to Queens exhibit saturated intensifying hot spots, signaling a notable increase in RSSs ridership throughout 2022, surrounded by sporadic hot spots. Conversely, peripheral areas of New York City reveal diminishing cold spots, indicating a decrease in their intensity as cold spots. Furthermore, the study conducts separate spatial and temporal profiling. By presenting the spatiotemporal trends of RSSs, this research complements existing literature and provides valuable insights for more informed interventions. The study also highlights certain limitations that could be addressed in future endeavors.

A Computational Framework to Optimize the Mechanical Behavior of Synthetic Vascular Grafts.

The failure of synthetic small-diameter vascular grafts has been attributed to a mismatch in the compliance between the graft and native artery, driving mechanisms that promote thrombosis and neointimal hyperplasia. Additionally, the buckling of grafts results in large deformations that can lead to device failure. Although design features can be added to lessen the buckling potential, the addition is detrimental to decreasing compliance (e.g., reinforcing coil). Herein, we developed a novel finite element framework to inform vascular graft design by evaluating compliance and resistance to buckling. A batch-processing scheme iterated across the multi-dimensional design parameter space, which included three parameters: coil thickness, modulus, and spacing. Three types of finite element models were created in FEBio for each unique coil-reinforced graft parameter combination to simulate pressurization, axial buckling, and bent buckling, and results were analyzed to quantify compliance, buckling load, and kink radius, respectively, from each model. Importantly, model validation demonstrated that model predictions agree qualitatively and quantitatively with experimental observations. Subsequently, data for each design parameter combination were integrated into an optimization function for which a minimum value was sought. The optimization values identified various candidate graft designs with promising mechanical properties. Our investigation successfully demonstrated the model-directed framework identified vascular graft designs with optimal mechanical properties, which can potentially improve clinical outcomes by addressing device failure. In addition, the presented computational framework promotes model-directed device design for a broad range of biomaterial and regenerative medicine strategies.

Soliton and lump and travelling wave solutions of the (3 + 1) dimensional KPB like equation with analysis of chaotic behaviors

Nonlinear evolution equations (NLEEs) have a wide range of applications in various fields, including physics, engineering, biology, economics, and more. These equations are used to describe complex systems that change over time, where the state or behavior of the system not only depends on the current situation, but may also be related to the past. A deep understanding of the solutions to NLEEs is of great significance for predicting and controlling the behavior of complex systems. The (3 + 1)-dimensional Kadomtsev-Petviashvili-Boussinesq-like (KPB-like) equation represents a partial differential equation that describes nonlinear wave phenomena in multi-dimensional spaces. This model is commonly employed in fields such as fluid dynamics, plasma physics, and nonlinear optics to study wave behaviors. This paper investigates the KPB-like equations, which have meaningful physical implications in describing nonlinear wave phenomena. Hirota bilinear method is employed to derive the bilinear form for the KPB-like equation and 1-soliton, 2-soliton, lump, and travelling wave solutions are studied to this kind of nonlinear model. In addition, the chaotic behaviors of soliton and lump solutions are explored via applying the Duffing chaotic system. To have a better understanding of dynamic structures, 3D, line, density and contour map plots of begotten results are displayed. Our results indicate the directness and effectiveness of the applied method for analyzing high-dimensional differential equations that arise in nonlinear science.

Domain adaptation hyperspectral image fusion based on spatial-spectral domain separation

ABSTRACT Hyperspectral datasets captured by airborne are one of the important data sources in the field of hyperspectral image fusion. However, the limited number of data samples often hinders the optimal performance of deep learning-based methods on these datasets. Domain adaptation is expected to alleviate the issue of data scarcity. However, there are two issues that need to be addressed in applying domain adaptation to hyperspectral image fusion, which are the heterogeneity and spatial degradation diversity of hyperspectral data. In this paper, we propose a domain adaptation hyperspectral image fusion network based on spatial-spectral domain separation. The model, constructed with three-dimensional convolutional layers, effectively addresses the challenge of hyperspectral data heterogeneity. Compared with 2D convolution, 3D convolution is able to consider both spatial and spectral dimensions and extract spatial-spectral features efficiently. Based on this, we design a domain-separation architecture to extract domain-invariant and domain-private features in the spatial-spectral domain. The architecture achieves domain adaptation by extracting domain-invariant features from both datasets to obtain the prior knowledge in the source dataset and apply it to the target dataset. Additionally, the spatial degradation of different datasets varies due to distinct shooting conditions during the acquisition. Therefore, the fusion algorithms should be robust to various degradation scenarios. To tackle this challenge, we design the Observation Module to predict degradation information and the Degradation Information Modulation Module to apply it to the input, thereby enhancing the network’s robustness. Experiments on various datasets demonstrate that our method is qualitatively and quantitatively superior to state-of-the-art methods.

Criticality of the O(N) universality via global solutions to nonperturbative fixed-point equations

Fixed-point equations in the functional renormalization group approach are integrated from large to vanishing field, where an asymptotic potential in the limit of large field is implemented as initial conditions. This approach allows us to obtain a global fixed-point potential with high numerical accuracy, that incorporates the correct asymptotic behavior in the limit of large field. Our calculated global potential is in good agreement with the Taylor expansion in the region of small field, and it also coincides with the Laurent expansion in the regime of large field. Laurent expansion of the potential in the limit of large field for general case, that the spatial dimension d is a continuous variable in the range 2≤d≤4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\\le d \\le 4$$\\end{document}, is obtained. Eigenfunctions and eigenvalues of perturbations near the Wilson–Fisher fixed point are computed with the method of eigenperturbations. Critical exponents for different values of d and N of the O(N) universality class are calculated.