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22 pages, 2166 KB  
Article
Sound-to-Image Translation Through Direct Cross-Modal Connection Using a Convolutional–Attention Generative Model
by Leonardo A. Fanzeres, Climent Nadeu and José A. R. Fonollosa
Appl. Sci. 2026, 16(6), 2942; https://doi.org/10.3390/app16062942 - 18 Mar 2026
Viewed by 120
Abstract
Sound plays a fundamental role in human perception, conveying information about events, objects, and spatial dynamics that may not be visually accessible. However, current technologies such as Acoustic Event Detection typically reduce complex soundscapes to textual labels, often failing to preserve their semantic [...] Read more.
Sound plays a fundamental role in human perception, conveying information about events, objects, and spatial dynamics that may not be visually accessible. However, current technologies such as Acoustic Event Detection typically reduce complex soundscapes to textual labels, often failing to preserve their semantic richness. This limitation motivates the exploration of sound-to-image (S2I) translation as an alternative connection between audio and visual modalities. Unlike multimodal approaches guided by intermediary constraints during the learning process, we investigate S2I translation without class supervision, cluster-based alignment, or textual mediation, a paradigm we refer to as direct S2I translation. To the best of our knowledge, apart from our previous work, no prior study addresses S2I translation under this fully direct setting. We propose a convolutional–attention generative framework composed of an audio encoder and a densely connected GAN integrating self-attention and cross-attention mechanisms. The attention-based model is systematically compared with a purely convolutional baseline. Results show that introducing attention at early stages of the generator significantly improves translation performance, increasing the likelihood of producing interpretable and semantically coherent visual representations of sound. These findings indicate that attention strengthens semantic correspondence between audio and vision while preserving the fully direct nature of the translation process. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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24 pages, 8092 KB  
Article
Seismic Performance and Fragility Assessment of a Prefabricated Shear Wall System with Keyway Interlocking and Concentrated Reinforcement Connections
by Chao Deng, Wei Sun and Xiaoyong Luo
Buildings 2026, 16(6), 1201; https://doi.org/10.3390/buildings16061201 - 18 Mar 2026
Viewed by 173
Abstract
Prefabricated reinforced concrete shear wall structures have attracted significant attention due to their advantages in industrialized construction and sustainability. However, the structural performance of prefabricated shear wall systems still requires further investigation to ensure reliable seismic behavior under earthquake loading. In this study, [...] Read more.
Prefabricated reinforced concrete shear wall structures have attracted significant attention due to their advantages in industrialized construction and sustainability. However, the structural performance of prefabricated shear wall systems still requires further investigation to ensure reliable seismic behavior under earthquake loading. In this study, a fully prefabricated shear wall system incorporating keyway interlocking joints and concentrated reinforcement connections is proposed, and its nonlinear seismic behavior is systematically investigated through finite element modeling, parametric analysis, nonlinear time history analysis, and incremental dynamic analysis. The finite element models were validated against available experimental results and reproduced the hysteretic response, stiffness degradation, and load-carrying capacity with good agreement. The relative errors in peak load were within 5%, indicating the reliability of the adopted modeling approach. Parametric analyses indicate that axial compression ratio, concrete strength, and wall thickness significantly affect structural performance, while prefabricated walls exhibit slightly lower stiffness and strength than cast-in-place walls, with mean reduction factors of 0.88 and 0.91. An eight-story prefabricated shear wall building subjected to multiple scaled ground motions exhibits stable flexure-dominated deformation without joint sliding or soft-story mechanisms. Peak roof displacements reached 19.71 mm and 32.85 mm in the X and Y directions, with maximum interstory drift ratios of 1/892 and 1/724. These values are significantly smaller than the commonly adopted collapse drift limit of 1/120 specified in seismic design guidelines, indicating a relatively large deformation safety margin under the ground motions considered. Probabilistic seismic demand models were established based on both PGA and Sa(T1, 5%) intensity measures, showing strong correlations with the maximum interstory drift ratio. Fragility analysis demonstrates a high probability of remaining in intact or slight damage states under frequent and design-level earthquakes and a low collapse probability under rare earthquakes. These findings provide valuable insights for the design of next-generation prefabricated shear wall systems with mechanical interlocking joints and concentrated reinforcement connections. Full article
(This article belongs to the Section Building Structures)
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17 pages, 284 KB  
Article
Linear Hamiltonian Vector Fields on Lie Groups
by Víctor Ayala and María Luisa Torreblanca Todco
Mathematics 2026, 14(6), 994; https://doi.org/10.3390/math14060994 - 14 Mar 2026
Viewed by 200
Abstract
Linear vector fields on Lie groups constitute a fundamental class of dynamical systems, as their flows are one-parameter subgroups of automorphisms and their infinitesimal behavior is entirely determined by derivations of the Lie algebra. When a Lie group is endowed with a Hamiltonian-type [...] Read more.
Linear vector fields on Lie groups constitute a fundamental class of dynamical systems, as their flows are one-parameter subgroups of automorphisms and their infinitesimal behavior is entirely determined by derivations of the Lie algebra. When a Lie group is endowed with a Hamiltonian-type geometric structure, a natural problem is to determine whether such linear dynamics admit a global variational realization, and how such realizations can be interpreted in terms of reduced models of fluid motion. In the even-dimensional case, where the Lie group carries a symplectic structure, we establish a complete global criterion for the existence of Hamiltonians generating linear symplectic vector fields. The problem reduces to a single global obstruction: the de Rham cohomology class of the 1-form ιXω. Thus, every linear symplectic vector field on a simply connected Lie group is globally Hamiltonian, and when the obstruction vanishes, we provide an explicit constructive procedure to recover the Hamiltonian. On the affine group Aff+(1), this yields a fully explicit, finite-dimensional Hamiltonian model of a 1D ideal fluid with affine symmetries. We then treat odd-dimensional Lie groups, where symplectic geometry is unavailable. Using contact geometry as the canonical replacement, we prove a Hamiltonian lifting theorem ensuring the existence and uniqueness of the associated dynamics. The Reeb vector field appears as a distinguished vertical direction resolving the ambiguities of degenerate Hamiltonian systems. On the Heisenberg group H3, this gives a fully explicit contact Hamiltonian model of an effective non-conservative fluid mode. Finally, we interpret symplectic and contact theories within a unified geometric framework and discuss their relevance to geometric formulations of ideal (symplectic) and effective (contact) fluid equations on Lie groups. Full article
(This article belongs to the Special Issue Mathematical Fluid Dynamics: Theory, Analysis and Emerging Trends)
18 pages, 594 KB  
Article
Research on Hybrid Energy Storage Optimisation Strategies for Mitigating Wind Power Fluctuations
by Zhenyun Song and Yu Zhang
Algorithms 2026, 19(3), 204; https://doi.org/10.3390/a19030204 - 9 Mar 2026
Viewed by 206
Abstract
Wind power generation exhibits pronounced volatility and intermittency, and direct grid connection may cause instability in grid frequency. To address this issue, this paper proposes an optimisation strategy for hybrid energy storage systems to mitigate wind power fluctuations, integrating lithium-ion batteries with supercapacitors [...] Read more.
Wind power generation exhibits pronounced volatility and intermittency, and direct grid connection may cause instability in grid frequency. To address this issue, this paper proposes an optimisation strategy for hybrid energy storage systems to mitigate wind power fluctuations, integrating lithium-ion batteries with supercapacitors within wind power systems. Firstly, the grid-connected power of wind turbines and the reference power of the energy storage system are determined through dynamic weight adjustment using a weighted filtering algorithm combining adaptive exponential smoothing and recursive averaging algorithms. Secondly, the fish-eagle optimisation algorithm is employed to refine variational modal decomposition parameters. The modal components derived from decomposing the energy storage system’s reference power are converted into Hilbert marginal spectra. Following determination of the cut-off frequency, high-frequency signal components are managed by supercapacitors, while low-frequency components are handled by lithium-ion batteries. Finally, an optimised configuration model for the hybrid energy storage system is constructed to minimise the annual lifecycle target cost. Case study analysis demonstrates that this approach effectively smooths fluctuations in wind power output while fully leveraging the complementary characteristics of both energy storage types, achieving a balance between system economics and overall performance. Full article
(This article belongs to the Section Algorithms for Multidisciplinary Applications)
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19 pages, 5177 KB  
Article
Maritime Trajectory Forecasting via CNN–SOFTS-Based Coupled Spatio-Temporal Features
by Yongfeng Suo, Chunyu Yang, Gaocai Li, Qiang Mei and Lei Cui
Sensors 2026, 26(5), 1547; https://doi.org/10.3390/s26051547 - 1 Mar 2026
Viewed by 335
Abstract
Spatio-temporal features are crucial for maritime trajectory forecasting, especially in scenarios involving curved waterways or abrupt changes in ship motion patterns. Although Automatic Identification System (AIS) data, which are widely used for trajectory prediction, inherently include temporal and spatial information, effectively strengthening these [...] Read more.
Spatio-temporal features are crucial for maritime trajectory forecasting, especially in scenarios involving curved waterways or abrupt changes in ship motion patterns. Although Automatic Identification System (AIS) data, which are widely used for trajectory prediction, inherently include temporal and spatial information, effectively strengthening these features and integrating them into prediction models remains challenging. To address this challenge, we propose a Convolutional Neural Network (CNN)-Series-cOre Fused Time Series forecaster (SOFTS)-based framework that explicitly couples spatial and temporal features to achieve high-fidelity maritime trajectory forecasting, especially in scenarios with complex spatial patterns. We first employ a CNN-based spatial encoder to hierarchically abstract spatial density distributions through convolution and pooling operations, thereby learning global spatial structure patterns of ship movements. This encoder emphasizes overall spatial morphology rather than precise individual trajectory points. Second, we employ the SOFTS model to incorporate angular velocity, acceleration, and angular acceleration as input features to characterize ship motion states, which can capture the temporal dependencies of ship motion states from multivariate time series. Finally, the spatial embedding features extracted by the CNN are concatenated with the temporal feature representations learned by SOFTS along the feature dimension to form a joint spatiotemporal representation. This representation is then fed into a fusion regression module composed of fully connected layers to predict future ship trajectories. Experimental results on the validation dataset show that the proposed method achieves an MSE of 0.020 and an MAE of 0.060, outperforming several advanced time series forecasting models in prediction accuracy and computational efficiency. The introduction of angular velocity, acceleration, and angular acceleration features reduces the MSE and MAE by approximately 10.22% and 9.49%, respectively, validating the effectiveness of the introduced dynamic features in improving trajectory prediction performance. These results underscore the proposed method’s potential for intelligent navigation and traffic management systems by effectively enhancing inland river navigation safety and strengthening waterborne traffic monitoring capabilities. Full article
(This article belongs to the Section Navigation and Positioning)
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17 pages, 2481 KB  
Article
Soft Sensor Model of f-CaO Content in Cement Clinker Based on Self-Attention and Time Convolutional Network
by Siyuan Zhou and Le Yang
Information 2026, 17(3), 230; https://doi.org/10.3390/info17030230 - 1 Mar 2026
Viewed by 246
Abstract
The quality of cement clinker is strongly linked to its free calcium oxide (f-CaO) content. Therefore, real-time detection of f-CaO content is crucial for reducing energy consumption and stabilizing clinker quality. This work presents a Temporal Convolutional Network (TCN) that incorporates a self-attention [...] Read more.
The quality of cement clinker is strongly linked to its free calcium oxide (f-CaO) content. Therefore, real-time detection of f-CaO content is crucial for reducing energy consumption and stabilizing clinker quality. This work presents a Temporal Convolutional Network (TCN) that incorporates a self-attention mechanism for handling coupled time-series data from process variables. This model utilizes TCN to capture the time series coupling relationship among multiple input variables and extract multivariable time series features that affect f-CaO content. On this basis, a self-attention mechanism is introduced to focus on nonlinear features that have a significant impact on the output variable. The self-attention mechanism enhances the model’s ability through three key aspects: dynamic feature weighting, global context awareness, and interpretable feature selection. Combined with TCN’s time feature extraction, a robust f-CaO content prediction framework is constructed. Finally, a mapping relationship between nonlinear features and output is established through a fully connected layer, enabling real-time measurement of f-CaO content. Experimental comparisons with existing deep learning-based soft sensors demonstrate the superior performance of our model. Full article
(This article belongs to the Special Issue New Deep Learning Approach for Time Series Forecasting, 2nd Edition)
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16 pages, 4906 KB  
Article
Non-Human Primates in Gabon: Occurrence Hotspots, Habitat Dynamics, Protected-Area Performance, and Conservation Challenges
by Mohamed Hassani Mohamed-Djawad, Barthelemy Ngoubangoye, Papa Ibnou Ndiaye, Krista Mapagha-Boundoukou, Neil Michel Longo-Pendy, Serge Ely Dibakou, Jean Nzue-Nguema, Désiré Otsaghe-Ekore, Stephan Ntie, Afred Ngomanda, Patrice Makouloutou-Nzassi, Mohamed Thani Ibouroi and Larson Boundenga
Biology 2026, 15(5), 405; https://doi.org/10.3390/biology15050405 - 28 Feb 2026
Viewed by 351
Abstract
Gabon harbors one of Africa’s richest assemblages of non-human primates (NHPs), yet integrated national-scale evidence on their conservation status remains limited. To inform conservation strategies, we conducted the first nationwide assessment integrating habitat dynamics, the geographic distribution of species, and the effectiveness of [...] Read more.
Gabon harbors one of Africa’s richest assemblages of non-human primates (NHPs), yet integrated national-scale evidence on their conservation status remains limited. To inform conservation strategies, we conducted the first nationwide assessment integrating habitat dynamics, the geographic distribution of species, and the effectiveness of the protected-area network in the country. We harmonized 300 m land-cover maps (ESA CCI 1992; Copernicus 2022), compiled 481 georeferenced occurrences, and identified concentration areas using kernel density estimation and Getis–Ord Gi* analysis. We quantified land-cover transitions with a per-pixel transition matrix and assessed protected-area capture using Monte Carlo randomization. Ten fully protected species are confirmed, including Gorilla gorilla and Pan troglodytes. Occurrences concentrate mainly in the Ogooué-Ivindo and Haut-Ogooué Provinces; ~10% of the national territory lies above the 90th kernel density percentile (≈26,700 km2), and 1.5% of cells qualify as hotspots at the 99% threshold. Primate records are strongly associated with evergreen broadleaved forests (87.9% of points), which remained persistent from 1992 to 2022 (forest-to-forest = 223,476 km2; 98.13%) with a net decline (−2571.66 km2; −1.19%). Gross losses (4046.58 km2) were mainly attributable to agricultural conversion (68.63%; χ2 = 31,525; p < 0.001). Over 90% of records fall in areas stable across 1992–2022. Protected areas (PAs) captured more occurrences (observed 40.1% vs. expected 18.47%; p < 0.001), yet gaps remain for some taxa (e.g., Allochorocebus solatus, 86% outside PAs). Overall, Gabon retains an extensive core of suitable habitat, but targeted action outside PAs and maintenance of landscape connectivity are needed to secure populations where agricultural expansion and fragmentation are intensifying. Full article
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24 pages, 5580 KB  
Article
DF-TransVAE: A Deep Fusion Network for Binary Classification-Based Anomaly Detection in Internet User Behavior
by Huihui Fan, Yuan Jia, Wu Le, Zhenhong Jia, Hui Zhao, Congbing He, Hedong Jiang, Zeyu Hu, Xiaoyi Lv, Jianting Yuan and Xiaohui Huang
Appl. Sci. 2026, 16(5), 2243; https://doi.org/10.3390/app16052243 - 26 Feb 2026
Viewed by 239
Abstract
User behavior anomaly detection plays a vital role in network security for identifying malicious access and abnormal activities in high-dimensional internet user behavior data. Although Transformer architectures have been widely adopted in anomaly detection tasks, and their integration with Variational Autoencoders (VAEs) has [...] Read more.
User behavior anomaly detection plays a vital role in network security for identifying malicious access and abnormal activities in high-dimensional internet user behavior data. Although Transformer architectures have been widely adopted in anomaly detection tasks, and their integration with Variational Autoencoders (VAEs) has often been used to further improve detection accuracy, existing integration methods have failed to effectively balance global feature dependency modeling and generative data distribution learning. This results in limited capability in identifying complex anomalous patterns. To address this issue, this paper proposes DF-TransVAE, a novel deeply integrated framework that advances the integration of a Transformer and a VAE for supervised anomaly detection. The framework first fuses global contextual representations from the Transformer encoder with original input features, then maps the fused representation into the latent space via the VAE encoder. A cross-attention mechanism is introduced as the core of deep integration, enabling dynamic, bidirectional interaction between the fused features and latent variables to enhance information fusion. Lastly, a fully connected classifier equipped with residual connections outputs anomaly probabilities for supervised binary classification. Experimental results on two public datasets demonstrate that the proposed framework achieves better performance than existing deep learning methods in terms of accuracy, precision, recall, and F1-score, particularly in detecting complex anomalous patterns. Our results indicate that the deep integration mechanism we propose effectively addresses the limitations of conventional Transformer–VAE combinations. Full article
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44 pages, 3240 KB  
Article
Event-Triggered Distributed Variable Admittance Control for Human–Multi-Robot Collaborative Manipulation
by Mohammad Jahani Moghaddam and Filippo Arrichiello
Robotics 2026, 15(3), 48; https://doi.org/10.3390/robotics15030048 - 25 Feb 2026
Viewed by 289
Abstract
In this paper, we propose a distributed admittance control framework for joint manipulation of objects by multiple robotic arms that addresses the challenges of human–robot interaction. The system is developed to control the joint transportation of an object by N Franka Emika Panda [...] Read more.
In this paper, we propose a distributed admittance control framework for joint manipulation of objects by multiple robotic arms that addresses the challenges of human–robot interaction. The system is developed to control the joint transportation of an object by N Franka Emika Panda robots (validated with up to four in simulations) using external human force estimation in a distributed manner without relying on centralized computation or force sensors. We integrate a hybrid observer by combining a distributed force estimator with a nonlinear disturbance observer (NDOB) to achieve accurate human force estimation and minimize estimation errors in simulations. Adaptive radial basis function neural networks (RBFNNs) are employed to dynamically adjust the damping and inertia parameters, enhancing the system’s adaptability and stability. Event-based communication minimizes network bandwidth usage, while consensus protocols ensure synchronization of state estimates across robots. Unlike conventional methods, the proposed observer operates in a fully sensorless manner: no human-force measurements are required. The estimation relies solely on locally available robot states, maintaining high accuracy while reducing system complexity. The framework demonstrates scalability to multiple robots, enhancing robustness in distributed settings. Simulation results show superior performance in terms of path tracking, force estimation accuracy, and communication efficiency compared to centralized approaches. Specifically, the event-triggered strategy reduces communication messages by approximately 70% compared to always-connected mode while maintaining comparable RMSE in position (9.97×105 vs. 7.39×105) and velocity (2.52×105 vs. 3.76×105), outperforming periodic communication. Full article
(This article belongs to the Section Sensors and Control in Robotics)
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26 pages, 4461 KB  
Article
A Spatiotemporal Feature-Driven Deep Learning Framework for Fine-Grained Tugboat Operation Recognition
by Xiang Jia, Hongxiang Feng, Manel Grifoll and Qin Lin
Systems 2026, 14(2), 225; https://doi.org/10.3390/systems14020225 - 23 Feb 2026
Viewed by 230
Abstract
Accurate perception of tugboat operational status is essential for optimising port scheduling efficiency and ensuring operational safety. However, existing AIS-based methods often struggle to capture the fine-grained and asymmetric manoeuvring characteristics of tugboats, particularly in distinguishing assisted berthing from unberthing operations. To address [...] Read more.
Accurate perception of tugboat operational status is essential for optimising port scheduling efficiency and ensuring operational safety. However, existing AIS-based methods often struggle to capture the fine-grained and asymmetric manoeuvring characteristics of tugboats, particularly in distinguishing assisted berthing from unberthing operations. To address these limitations, this study proposes a hybrid recognition framework integrating multidimensional feature engineering with spatiotemporal dynamics. First, a speed-threshold-based sliding window algorithm segments trajectories into sailing and berthing states. Second, a 15-dimensional feature vector—comprising statistical and descriptive features from speed, heading, and trajectory morphology—is constructed to characterise tugboat behaviour. Notably, morpho-logical descriptors such as the ‘Overlap Ratio’ serve as implicit spatial proxies, capturing geographical constraints without reliance on Electronic Navigational Charts. A three-layer fully connected neural network (FCNN) is then developed to classify segments into “Cruising” and “Assisting in Berthing/Unberthing.” Finally, a speed-dynamics rule further distinguishes berthing from unberthing based on opposing temporal evolution patterns. Experiments on real AIS data from Ningbo–Zhoushan Port demonstrate that the model achieves an F1-score of 0.90 and a recall of 0.93 for assistance-related operations. Permutation importance analysis confirms that integrating kinematic and morphological features enables interpretable and precise intent inference. This study offers a high-precision, low-dependency solution for tugboat operation identification, supporting intelligent port surveillance and sustainable maritime management. Full article
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28 pages, 9511 KB  
Article
Informing Strategic Planning Under Uncertainty: Using Rao’s Q Index on Scenario Rankings to Assess Landscape Stability and Vulnerability
by Raffaele Pelorosso, Sergio Noce, Francesco Cappelli, Duccio Rocchini, Federica Gobattoni, Ciro Apollonio, Andrea Petroselli, Fabio Recanatesi and Maria Nicolina Ripa
Land 2026, 15(2), 319; https://doi.org/10.3390/land15020319 - 13 Feb 2026
Viewed by 373
Abstract
Scenario planning supports strategic decision-making under uncertainty by comparing multiple plausible futures. Impact indicators help to prioritize scenarios, while rank-based evaluations clearly communicate indicator relevance for participatory planning, policymaking, and resource allocation. Ensuring that rankings are both sensitive and robust is therefore essential. [...] Read more.
Scenario planning supports strategic decision-making under uncertainty by comparing multiple plausible futures. Impact indicators help to prioritize scenarios, while rank-based evaluations clearly communicate indicator relevance for participatory planning, policymaking, and resource allocation. Ensuring that rankings are both sensitive and robust is therefore essential. However, conventional statistical measures fail to fully capture ranking dynamics. They describe overall dispersion but cannot jointly assess the magnitude of rank shifts and the frequency with which items occupy specific ranks across scenarios. This study explores the novel application of Rao’s Quadratic Entropy (Rao’s Q) in scenario analysis to quantify ranking variability. A theoretical test demonstrates that Rao’s Q captures full variability in rankings and continuous values, suggesting it as a promising alternative to existing approaches. Rao’s Q is then applied to a climate change hotspot in Central Italy to evaluate changes in bio-energy landscape connectivity across forty-eight scenarios. Results reveal how land-use and climate changes affect landscape unit connectivity over time, identifying which are highly stable across scenarios or consistently critical, and thus highlighting planning priorities for mitigation, conservation, and sustainable urban development. Supported by openly available R code, this study demonstrates the relevance of Rao’s Q for participatory, scenario-based decision-making processes. Full article
(This article belongs to the Special Issue The Relationship Between Landscape Sustainability and Urban Ecology)
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18 pages, 333 KB  
Article
A Small Patch Hypothesis in Cosmology
by Meir Shimon
Astronomy 2026, 5(1), 4; https://doi.org/10.3390/astronomy5010004 - 9 Feb 2026
Viewed by 383
Abstract
If our observable Universe is only a tiny region of a vastly larger and conformally older spacetime, then the usual formulations of the classical flatness and horizon problems of the Hot Big Bang can be reinterpreted as artifacts manifesting an observational selection effect; [...] Read more.
If our observable Universe is only a tiny region of a vastly larger and conformally older spacetime, then the usual formulations of the classical flatness and horizon problems of the Hot Big Bang can be reinterpreted as artifacts manifesting an observational selection effect; we occupy a small causal domain of a much larger causally-connected and possibly non-flat spacetime. A sufficiently large positive cosmological constant, Λ, sets the future asymptotic horizon scale of the observable Universe, ∼Λ1/2, thereby implying that the observable Universe may simply be a minute patch of a far larger pre-existing one, hereafter a Small Patch Hypothesis. Importantly, this observational bound is purely geometric; regardless of when the Universe is observed, the maximum accessible scale is finite and fixed by Λ, independent of inflationary dynamics, anthropic arguments, or assumptions about the global hosting spacetime. The externally possibly frozen past-eternal state implied by a pre-existing, causally connected spacetime motivates, but does not strictly require, viewing the perturbation field as being in (or arbitrarily close to) a coarse-grained maximum-entropy—equilibrium—configuration. Conditionalizing only on fixed mean and variance, a Gaussian distribution uniquely emerges, while the absence of entropy gradients corresponds to adiabaticity. In this work these features are therefore treated as plausible maximum-ignorance priors for super-horizon perturbations, rather than as rigorously derived consequences of a fully developed microscopic notion of gravitational entropy. In this sense, inflation becomes one viable realization of the proposed Small Patch Hypothesis. Here, one particular non-inflationary alternative is considered for illustrative purposes in which a primordial spectrum Pζ(k) of the gauge-invariant perturbation ζ that pre-dates the Big Bang grows logarithmically toward large scales, k0, and in fact diverges at some finite kc. If kcΛ1/2, then our local cosmic patch probes only the regime where ζ1 and appears exceptionally smooth. Over the comparatively narrow observable window, this Pζ(k) mimics a slightly red-tilted, inflation-like spectrum. Rather than introducing high-energy new fields, this perspective frames large-scale homogeneity, isotropy, Gaussianity, adiabaticity, and the observed thermodynamic Arrow of Time as possible consequences of restricted observational access to a much larger Universe in equilibrium, rather than signatures of a unique early-Universe mechanism. Current observations cannot distinguish this logarithmically running spectrum from the standard power-law one, but future probes—for example high-resolution 21-cm measurements of the Dark Ages—may be able to falsify it. Full article
34 pages, 489 KB  
Article
Gauge-Invariant Gravitational Wave Polarization in Metric f(R) Gravity with Cosmological Implications
by Ramesh Radhakrishnan, David McNutt, Delaram Mirfendereski, Alejandro Pinero, Eric Davis, William Julius and Gerald Cleaver
Universe 2026, 12(2), 44; https://doi.org/10.3390/universe12020044 - 5 Feb 2026
Viewed by 827
Abstract
We develop a fully gauge-invariant analysis of gravitational-wave polarizations in metric f(R) gravity with a particular focus on the modified Starobinsky model f(R)=R+αR22Λ, whose constant-curvature solution [...] Read more.
We develop a fully gauge-invariant analysis of gravitational-wave polarizations in metric f(R) gravity with a particular focus on the modified Starobinsky model f(R)=R+αR22Λ, whose constant-curvature solution Rd=4Λ provides a natural de Sitter background for both early- and late-time cosmology. Linearizing the field equations around this background, we derive the Klein–Gordon equation for the curvature perturbation δR and show that the scalar propagating mode acquires a mass mψ2=1/(6α), highlighting how the same scalar degree of freedom governs inflationary dynamics at high curvature and the propagation of gravitational waves in the current accelerating Universe. Using the scalar–vector–tensor decomposition and a decomposition of the perturbed Ricci tensor, we obtain a set of fully gauge-invariant propagation equations that isolate the contributions of the scalar, vector, and tensor modes in the presence of matter. We find that the tensor sector retains the two transverse–traceless polarizations of General Relativity, while the scalar sector contains an additional massive scalar propagating degree of freedom, which manifests through breathing and longitudinal tidal responses depending on the wave regime and detector frame. Through the geodesic deviation equation—computed both in a local Minkowski patch and in fully covariant de Sitter form—we independently recover the same polarization content and identify its tidal signatures. The resulting framework connects the extra scalar polarization to cosmological observables: the massive scalar propagating mode sets the range of the fifth force, influences the time evolution of gravitational potentials, and affects the propagation and dispersion of gravitational waves on cosmological scales. This provides a unified, gauge-invariant link between gravitational-wave phenomenology and the cosmological implications of metric f(R) gravity. Full article
(This article belongs to the Section Gravitation)
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26 pages, 4800 KB  
Article
Porosity and Permeability Estimations from X-Ray Tomography Images and Data Using a Deep Learning Approach
by Edwar Herrera, Oriol Oms and Eduard Remacha
Appl. Sci. 2026, 16(3), 1613; https://doi.org/10.3390/app16031613 - 5 Feb 2026
Viewed by 468
Abstract
This work presents a novel deep learning workflow for estimating porosity and permeability from combined data, where numerical variables such as high-resolution bulk density (RHOB) and photoelectric factor (PEF) data are integrated with X-ray computed tomography (X-CT) image data, using a dual-energy X-CT [...] Read more.
This work presents a novel deep learning workflow for estimating porosity and permeability from combined data, where numerical variables such as high-resolution bulk density (RHOB) and photoelectric factor (PEF) data are integrated with X-ray computed tomography (X-CT) image data, using a dual-energy X-CT approach (DECT). Convolutional neural networks (CNNs) were calibrated with routine core analysis (RCAL) laboratory measurements from one well from Sinú-San Jacinto Basin (Colombia). The CNN architecture combines two main branches: An image branch, in which a CNN extracts spatial features from normalized X-CT sections using 3 × 3 convolution layers, ReLU activation, batch normalization, and maxPooling, and a numerical branch, which processes the input vectors corresponding to RHOB and PEF using fully connected dense layers and dropout regularization. Both branches are concatenated in a fusion layer, from which the model’s final predictions are made. Results indicate a strong correlation between porosity, permeability, RHOB and PEF logs, and CT images. The porosity model achieved excellent predictive performance, with an R2 = 0.996, MAE = 3.96 × 10−3, MSE = 3.82 × 10−5, and 0.064 maximum error. The permeability model also performed well, with a linear R2 = 0.983, though metrics reflected the wide dynamic range of permeability. Consequently, artificial neural networks (ANNs) can accurately predict porosity and permeability at various depths where no corresponding laboratory data exists, demonstrating excellent predictive capabilities over several rock intervals, in a high vertical resolution because of X-CT data scale (0.625 mm). Full article
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17 pages, 920 KB  
Review
Integrating Single-Cell and Spatial Multi-Omics to Decode Plant–Microbe Interactions at Cellular Resolution
by Yaohua Li, Jared Vigil, Rajashree Pradhan, Jie Zhu and Marc Libault
Microorganisms 2026, 14(2), 380; https://doi.org/10.3390/microorganisms14020380 - 5 Feb 2026
Viewed by 901
Abstract
Understanding the intimate interactions between plants and their microbiota at the cellular level is essential for unlocking the full potential of plant holobionts in agricultural systems. Traditional bulk and microbial community-level sequencing approaches reveal broad community patterns but fail to resolve how distinct [...] Read more.
Understanding the intimate interactions between plants and their microbiota at the cellular level is essential for unlocking the full potential of plant holobionts in agricultural systems. Traditional bulk and microbial community-level sequencing approaches reveal broad community patterns but fail to resolve how distinct plant cell types interact with or regulate microbial colonization, as well as the diverse antagonistic and synergistic interactions and responses existing between various microbial populations. Recent advances in single-cell and spatial multi-omics have transformed our understanding of plant cell identities as well as gene regulatory programs and their dynamic regulation in response to environmental stresses and plant development. In this review, we highlight the single-cell discoveries that uncover the plant cell-type-specific microbial perception, immune activation, and symbiotic differentiation, particularly in roots, nodules, and leaves. We further discuss how integrating transcriptomic, epigenomic, and spatial data can reconstruct multilayered interaction networks that connect plant cell-type-specific regulatory states with microbial spatial niches and inter-kingdom signaling (e.g., ligand–receptor and metabolite exchange), providing a foundation for developing new strategies to engineer crop–microbiome interactions to support sustainable agriculture. We conclude by outlining key methodological challenges and future research priorities that point toward building a fully integrated cellular interactome of the plant holobiont. Full article
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