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Keywords = empirical formulation

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16 pages, 3570 KB  
Article
Data-Driven Robust Kalman Filter-Based Fault Detection for Traction Drive Systems
by Caixin Fu, Changhong Jiang, Zhiwei Wan, Peng Cheng and Shenquan Wang
Machines 2026, 14(5), 465; https://doi.org/10.3390/machines14050465 - 22 Apr 2026
Abstract
This article addresses the fault detection (FD) problem for traction drive systems in the presence of unknown noise covariances. The dynamic behavior of the traction drive system, affected by actuator and sensor faults, is first formulated. Following the philosophy of the subspace identification, [...] Read more.
This article addresses the fault detection (FD) problem for traction drive systems in the presence of unknown noise covariances. The dynamic behavior of the traction drive system, affected by actuator and sensor faults, is first formulated. Following the philosophy of the subspace identification, the system matrices are identified directly from collected process data using QR decomposition and singular value decomposition. Based on the identified model, a robust Kalman filter (KF)-based FD scheme is developed. By exploiting the iterative interaction between the estimator and measurement data within the KF framework, the noise covariance matrices are adaptively estimated, which alleviates the adverse effects caused by empirical covariance selection in conventional KF-based FD methods. Experimental results obtained from a real traction drive system verify the effectiveness and reliability of the proposed approach. Full article
(This article belongs to the Section Machines Testing and Maintenance)
19 pages, 1979 KB  
Article
Decoupling Economic Growth from Ecological Footprint in Brazil: The Roles of Biomass Energy, Resource Efficiency, Environmental Policy, and Energy Depletion
by Idris Awaidat Ajaj and Wagdi M. S. Khalifa
Sustainability 2026, 18(9), 4156; https://doi.org/10.3390/su18094156 - 22 Apr 2026
Abstract
The relationship between economic development and environmental degradation in Brazil was studied over the period 1970–2022, using ecological footprint (EF) as an environmental indicator. A contribution to the scientific literature exists here because biomass energy (BIO) has been separated from other types of [...] Read more.
The relationship between economic development and environmental degradation in Brazil was studied over the period 1970–2022, using ecological footprint (EF) as an environmental indicator. A contribution to the scientific literature exists here because biomass energy (BIO) has been separated from other types of renewable energy sources, and environmental policy stringency (EPS) and energy depletion (END) have been simultaneously analyzed for their joint impacts on EF in Brazil. In this research, four hypotheses were formulated for the relationships of: GDP, BIO, EPS, RE, and END with EF. The ARDL method was used in this analysis due to the different orders of integration for some of the variables and sample size limitations, both of which make alternative cointegration techniques inappropriate. All four hypotheses were supported in the empirical estimates of this study. In the long run, increases in GDP will result in increased EF, decreases in BIO and EPS will decrease EF, and no long-run relationship exists between RE and EF. However, RE has a short-term rebound effect. Increases in END will increase EF, indicating the environmental costs associated with the extraction and consumption of non-renewable resources. The statistically significant error correction term also supports the idea that there will be a quick adjustment towards the long-run equilibrium. The implications of these results suggest that Brazil continues to operate within a stage of growth driven primarily by scale rather than intensity, yet well-regulated biomass energy and strict environmental regulations provide a pathway for achieving decoupling in alignment with SDG 13 and SDG 15. Full article
(This article belongs to the Section Energy Sustainability)
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26 pages, 7247 KB  
Article
Fast Unconstraint Convex Symmetric Matrix for Semi-Supervised Learning
by Wenhao Wang, Kaiwen Chen, Wenjun Luo, Nan Zhou and Yanyi Cao
Symmetry 2026, 18(4), 698; https://doi.org/10.3390/sym18040698 - 21 Apr 2026
Abstract
Symmetric matrix factorization (SMF) plays an important role in clustering and representation learning. Nevertheless, most existing SMF-based approaches are formulated as non-convex optimization problems, which often leads to unstable convergence and high computational costs. In this paper, we develop a fast unconstrained convex [...] Read more.
Symmetric matrix factorization (SMF) plays an important role in clustering and representation learning. Nevertheless, most existing SMF-based approaches are formulated as non-convex optimization problems, which often leads to unstable convergence and high computational costs. In this paper, we develop a fast unconstrained convex symmetric matrix factorization framework, termed FUCSMF, for semi-supervised learning. By incorporating label information into the symmetric factorization formulation, the proposed model is transformed into a convex objective, which guarantees global optimality and enables efficient optimization using standard unconstrained solvers. To further improve scalability, a bipartite graph structure is introduced into SMF from a hypergraph-inspired perspective, significantly reducing the computational burden. The resulting computational complexity is reduced to O(nmd), which is substantially lower than the O(nmd+m2n+m3) complexity required by existing bipartite graph-based methods, where n, m, and d denote the numbers of samples, anchor points, and feature dimensions, respectively. In addition, we propose a correntropy-based graph construction strategy to alleviate the sensitivity of conventional adaptive neighbor bipartite graph methods. Extensive experiments on six benchmark datasets, involving comparisons with eleven state-of-the-art methods, demonstrate that FUCSMF achieves superior clustering performance while requiring significantly less computational time. Empirical results further show that the proposed method converges rapidly, typically within ten iterations. Full article
(This article belongs to the Section Computer)
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33 pages, 3266 KB  
Article
Digital Transformation and Sustainable Land Systems: The Non-Linear Impact of Information Infrastructure on Air Quality and Carbon Mitigation
by Hongyan Duan and Weidong Li
Land 2026, 15(4), 687; https://doi.org/10.3390/land15040687 - 21 Apr 2026
Abstract
As the digital economy advances, information infrastructure has become a core engine for driving green economic transition and optimizing sustainable land systems. However, its heterogeneous governance effects on different types of pollutants and spatial spillover mechanisms remain insufficiently explored. This study draws on [...] Read more.
As the digital economy advances, information infrastructure has become a core engine for driving green economic transition and optimizing sustainable land systems. However, its heterogeneous governance effects on different types of pollutants and spatial spillover mechanisms remain insufficiently explored. This study draws on the theoretical framework of the dynamic game between scale and technique effects. It utilizes the PSTR model and the SDM to systematically investigate the nonlinear and spatial synergistic impacts of information infrastructure. The analysis covers aggregate information infrastructure and its structural subdivisions, including traditional and new information infrastructure. To ensure empirical rigor, this study introduces a Bartik instrumental variable constructed via the shift share approach and thoroughly eliminates endogeneity interference through the Control Function Approach and a core variable lagging strategy. The empirical research reveals three core findings. Firstly, after crossing the initial extensive scale effect dominated by physical construction, the profound technique effect dominates long-term environmental governance. Secondly, new-type information infrastructure demonstrates a superior capacity for long-term environmental governance and land use efficiency compared to traditional telecommunications. Finally, spatial spillover analysis indicates that although PM2.5 exhibits strong cross-regional physical contagion, the current environmental dividends of information infrastructure remain highly localized due to regional administrative data silos, lacking significant cross-regional synergistic spillover effects. This study provides a solid empirical basis for formulating differentiated digital spatial governance frameworks, breaking interprovincial data factor barriers, and preventing the physical expansion trap of traditional infrastructure. Full article
(This article belongs to the Section Land Systems and Global Change)
33 pages, 354 KB  
Article
How Does R&D Investment Persistence Boost SRUN Firms’ Growth Quality? A Mediation Analysis
by Xifeng Wang and Guocai Wang
Sustainability 2026, 18(8), 4107; https://doi.org/10.3390/su18084107 - 20 Apr 2026
Abstract
Specialized, Refined, Unique and Novel (SRUN) listed firms are pivotal to the high-quality development of China’s real economy, and their growth quality underpins the security of industrial and supply chains. This study empirically examines the relationship between R&D investment persistence and growth quality [...] Read more.
Specialized, Refined, Unique and Novel (SRUN) listed firms are pivotal to the high-quality development of China’s real economy, and their growth quality underpins the security of industrial and supply chains. This study empirically examines the relationship between R&D investment persistence and growth quality of Chinese A-share SRUN listed firms from 2006 to 2024, with technology conversion efficiency as the mediating variable. R&D investment persistence is measured from the dual dimensions of investment intensity and stability, and firm growth quality is a comprehensive indicator constructed via principal component analysis (PCA) from revenue growth, profitability and risk resilience. Panel data regression models, combined with mechanism, endogeneity, robustness and heterogeneity tests, are adopted for empirical analysis. The results show a significantly positive correlation between R&D investment persistence and SRUN firms’ growth quality, with the regression coefficient of R&D investment persistence on growth quality reaching 0.189 (p < 0.01); both investment intensity and stability exert significant positive effects on all dimensions of growth quality, with their regression coefficients on growth quality being 0.156 and 0.132 (both p < 0.01) respectively. Technology conversion efficiency plays a partial mediating role in this relationship, with the mediating effect ratio of R&D investment persistence on growth quality through technology conversion efficiency at 34.2%, as R&D investment persistence indirectly improves growth quality by enhancing patent output and new product conversion efficiency. Heterogeneity analysis indicates that this positive correlation is more pronounced in high-tech industries, small and medium-sized enterprises (SMEs) and eastern China-based firms, driven by differences in industrial R&D dependence, resource endowments and financing frictions. Though endogeneity is mitigated by instrumental variables, propensity score matching (PSM) and difference-in-differences (DID), strict causal identification is constrained by data availability. This study enriches the theories of R&D investment and firm growth, and provides empirical insights for SRUN firms to optimize their R&D strategies and for the government to formulate targeted support policies, so as to promote the high-quality development of SRUN firms and the transformation of China’s manufacturing industry. Full article
29 pages, 4014 KB  
Article
Differences and Analysis of Pressurised Water Reactor Containment Design Using Code ACI 349 and Code ACI 359
by Wenli Jiang and Shen Wang
Appl. Sci. 2026, 16(8), 4001; https://doi.org/10.3390/app16084001 - 20 Apr 2026
Abstract
The prestressed concrete containment structure constitutes the core protective structure of a nuclear power plant. This paper utilises the prestressed concrete containment vessel (PCCV) of the Hualong Pressurised Reactor 1000 (HPR-1000)—a third-generation pressurised water reactor (PWR)—as the primary research prototype. Utilising ANSYS, a [...] Read more.
The prestressed concrete containment structure constitutes the core protective structure of a nuclear power plant. This paper utilises the prestressed concrete containment vessel (PCCV) of the Hualong Pressurised Reactor 1000 (HPR-1000)—a third-generation pressurised water reactor (PWR)—as the primary research prototype. Utilising ANSYS, a finite element model was established, with key points selected at critical locations such as the dome, cylinder, and base slab for stress analysis calculations. Reinforcement quantification derived from the design methodologies and analytical formulations prescribed in ACI 349 and ACI 359 were compared under various loading conditions. This investigation identified the core discrepancies and influencing factors between the two codes in reinforcement design, alongside a sensitivity analysis to identify key parameters affecting reinforcement design in different structural zones. The results indicate that discrepancies in reinforcement requirements stem primarily from the divergent design philosophies and strength assessment formulations, with this influence outweighing variations in load combinations. Furthermore, significant spatial differences exist in the sensitivity of reinforcement designs for key components to parameters such as the height-to-diameter ratio, shutdown seismic actions, accident pressure, and temperature effects. The conclusions of this study establish theoretical foundations and furnish empirical data to enhance the computational efficiency of prestressed concrete containment design for pressurised water reactor (PWR) facilities, while supporting the alignment of national and international regulatory standards. Furthermore, they serve as a technical reference for advancing nuclear power structural design practices. Full article
47 pages, 1640 KB  
Article
Carbon Emissions Modeling of Coal and Natural Gas Use in Poland’s Net-Zero Energy Transition
by Bożena Gajdzik, Radosław Wolniak, Dominik Bałaga and Wiesław Grebski
Resources 2026, 15(4), 58; https://doi.org/10.3390/resources15040058 - 20 Apr 2026
Abstract
This study develops econometric models to examine greenhouse gas emissions associated with coal and natural gas consumption in Poland between 2015 and 2023. Poland has one of the most carbon-intensive energy systems in Europe. Three complementary log–log econometric models were estimated: a model [...] Read more.
This study develops econometric models to examine greenhouse gas emissions associated with coal and natural gas consumption in Poland between 2015 and 2023. Poland has one of the most carbon-intensive energy systems in Europe. Three complementary log–log econometric models were estimated: a model explaining total CO2 emissions, a model assessing emission intensity (CO2 per unit of GDP), and a model capturing short-term variations in emission intensity. The results demonstrate that coal consumption remains the dominant determinant of absolute emissions, whereas the expansion of renewable energy significantly contributes to lowering the carbon intensity of economic growth. However, short-term fluctuations in emission intensity are still largely influenced by changes in fossil fuel consumption patterns. The findings highlight the gradual and sequential character of Poland’s energy transition, where gains in environmental efficiency precede a consistent reduction in total emissions. The proposed modeling framework offers an empirical basis for evaluating the effectiveness of climate and energy policies and can support the formulation of decarbonization strategies in economies heavily reliant on fossil fuels. Full article
(This article belongs to the Special Issue Assessment and Optimization of Energy Efficiency: 2nd Edition)
26 pages, 4364 KB  
Article
Tribological and Oxidation-Induced Degradation of Engine Materials Fueled with Bio-Hydrogenated Diesel–Biodiesel Blends
by Sathaporn Chuepeng, Atthaphon Maneedaeng, Niti Klinkaew, Anupap Pumpuang, Tanongsak Sukkasem and Ekarong Sukjit
Lubricants 2026, 14(4), 178; https://doi.org/10.3390/lubricants14040178 - 20 Apr 2026
Abstract
Although bio-hydrogenated diesel (BHD) offers drop-in compatibility and high oxidative stability, its poor lubricity remains a critical barrier to long-term engine deployment. Previous studies have primarily relied on short-term tribological assessments, leaving insufficient empirical data on sustained wear behavior under realistic conditions. This [...] Read more.
Although bio-hydrogenated diesel (BHD) offers drop-in compatibility and high oxidative stability, its poor lubricity remains a critical barrier to long-term engine deployment. Previous studies have primarily relied on short-term tribological assessments, leaving insufficient empirical data on sustained wear behavior under realistic conditions. This study addresses that gap through a 200 h durability evaluation of BHD–biodiesel blends in a single-cylinder diesel engine under constant load conditions per Thai Industrial Standard TIS 2618-2557. Five fuels, namely diesel, pure BHD, BHD90, BHD70, and pure biodiesel, were tested to identify the critical biodiesel threshold for optimal tribological and oxidative performance. BHD90 (90% BHD + 10% biodiesel) emerged as the optimal formulation, delivering the lowest torque reduction (11.2%) and minimal iron wear particles (101 ppm), while preserving oxidation stability. Biodiesel concentrations exceeding 10% induced accelerated lubricant oxidation through hygroscopic effects, negating the lubricity benefits. Fourier-transform infrared spectroscopy (FTIR) analysis of piston carbon deposits further revealed that higher biodiesel blends produced more oxygenated compounds, whereas pure BHD and diesel generated predominantly aliphatic hydrocarbons. These findings establish a mechanistic relationship between fuel composition, oxidation, and wear under endurance conditions, providing a practical guideline for renewable diesel formulation that balances lubrication performance, oxidation control, and long-term engine durability. Full article
(This article belongs to the Special Issue Tribological Impacts of Sustainable Fuels in Mobility Systems)
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11 pages, 220 KB  
Article
Effects of Different Proportions of Corn Silage and Ramie Silage on In Vitro Rumen Fermentation Characteristics and Methane Production
by Honghui Qi, Cheng Gao, Zhicai Li and Duanqin Wu
Animals 2026, 16(8), 1250; https://doi.org/10.3390/ani16081250 - 18 Apr 2026
Viewed by 147
Abstract
This study investigated the interactive effects of corn silage and ramie silage on in vitro rumen fermentation characteristics, aiming to provide a scientific basis and empirical evidence for the rational incorporation of ramie into ruminant diets. Four binary substrate mixtures were formulated based [...] Read more.
This study investigated the interactive effects of corn silage and ramie silage on in vitro rumen fermentation characteristics, aiming to provide a scientific basis and empirical evidence for the rational incorporation of ramie into ruminant diets. Four binary substrate mixtures were formulated based on dry matter (DM) mass ratios of corn silage to ramie silage: 100:0 (CON), 60:40 (R40), 20:80 (R80), and 0:100 (R100). Rumen fluid was collected from three adult Liuyang black goats surgically fitted with permanent rumen cannulas, and a standardized 48 h in vitro batch culture assay was conducted. Results demonstrated that increasing the proportion of ramie silage significantly decreased (p < 0.05) the DM degradation rate, neutral detergent fiber (NDF) degradation rate, acid detergent fiber (ADF) degradation rate, and total gas production per gram of substrate DM. Specifically, CON and R40 exhibited significantly higher values for all four parameters than R80 and R100 (p < 0.05). Methane production was significantly reduced in all ramie-containing treatments relative to CON (p < 0.05), whereas hydrogen production increased progressively with ramie inclusion level, with CON yielding significantly less H2 than both R80 and R100 (p < 0.05). Regarding fermentation parameters, increasing ramie proportion elevated (p < 0.05) both fermentation fluid pH and the acetate-to-propionate ratio, while total volatile fatty acid (TVFA) concentration declined linearly (p < 0.05). TVFA concentrations did not differ significantly between CON and R40, yet both were significantly greater than those in R80 and R100 (p < 0.05). Collectively, these findings indicate that ramie silage is a nutritionally valuable forage with potential as a high-quality partial replacement for conventional silages in ruminant feeding systems; however, its inclusion in corn–ramie mixed silages should not exceed 40% (on a DM basis) to maintain optimal fermentative efficiency and nutrient degradability. Full article
18 pages, 2343 KB  
Article
The Molecular Structures of Liquid and Glassy Nifedipine and Felodipine and Their Incorporation into PVP
by Chris J. Benmore, Stephen K. Wilke, Samrat Amin, Richard Weber, Pamela A. Smith, Stephen R. Byrn, Olivia Gibbons, Ethan Earl, Stephen Davidowski and Jeffery L. Yarger
Pharmaceuticals 2026, 19(4), 638; https://doi.org/10.3390/ph19040638 - 18 Apr 2026
Viewed by 165
Abstract
Background: Amorphous drug formulations are commonly used to improve the solubility and bioavailability of poorly soluble molecular pharmaceuticals, yet less is known about their molecular conformations and local bonding interactions than their crystalline phases. Methods: High-energy X-ray diffraction structure factor measurements [...] Read more.
Background: Amorphous drug formulations are commonly used to improve the solubility and bioavailability of poorly soluble molecular pharmaceuticals, yet less is known about their molecular conformations and local bonding interactions than their crystalline phases. Methods: High-energy X-ray diffraction structure factor measurements have been made on liquid and glassy nifedipine (NIF), felodipine (FEL), NIF 1:3 polyvinylpyrrolidone (PVP), and FEL 1:3 PVP wt.% mixtures. The corresponding X-ray pair distribution functions have been interpreted using empirical potential structure refinement using different models and density functional theory conformer calculations. Results: In both NIF and FEL, the NH···O inter-molecular hydrogen bonds between the pyridyl nitrogen and ester carbonyls are found to be considerably weaker than those observed in the crystalline polymorphs. For nifedipine, it is proposed that either inter-molecular NH…ON nitro bonds are present and/or a fraction (<20%) of conformational changes, with the aryl ring flipped, occur in the liquid state. For felodipine, the models indicate significant disorder associated with the methyl and ethyl side chains in the liquid state, with the main peak intensity at 3.0 Å arising from intra-molecular Cl-Cl atom pairs. When nifedipine molecules are incorporated into PVP, our models show they possess stronger NH···O bonds to the PVP polymer than felodipine molecules, which have stronger affinity for bonding to the polymer than to other felodipine molecules. Conclusions: The amorphous forms of both NIF and FEL show much weaker hydrogen bonding than found in their crystalline phases. Liquid NIF also exhibits configurations which are not observed in the crystal phases. Full article
(This article belongs to the Special Issue Crystal Engineering in the Pharmaceutical Sciences)
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28 pages, 1538 KB  
Article
A Risk-Aware Bidding Model for Air-Conditioned Building Users Participating in Demand Response Markets Based on Mental Accounting Theory
by Mengqiu Deng and Xiao Peng
Buildings 2026, 16(8), 1558; https://doi.org/10.3390/buildings16081558 - 15 Apr 2026
Viewed by 155
Abstract
Building users are key participants in demand response (DR) markets, providing significant flexible resources. Due to uncertainty in market clearing prices, various risk-based decision models have been developed to describe their bidding behavior, typically assuming constant risk preferences. However, empirical evidence indicates that [...] Read more.
Building users are key participants in demand response (DR) markets, providing significant flexible resources. Due to uncertainty in market clearing prices, various risk-based decision models have been developed to describe their bidding behavior, typically assuming constant risk preferences. However, empirical evidence indicates that users’ risk attitudes vary with the magnitude of load adjustments. To capture this feature, this paper introduces mental accounting theory to model the risk-aware bidding behavior of building users. Total response capacity is divided into three independent mental accounts based on air-conditioning setpoint adjustment magnitude, representing risk-averse, risk-neutral, and risk-seeking behaviors. This framework allows multiple risk preferences to be represented within a unified bidding model. For each account, response quantity and cost models are developed. Bidding strategies under uncertain market clearing prices are formulated by incorporating loss aversion. A multi-agent simulation framework, including building users, a load aggregator, and a grid operator, is established to simulate the market clearing process. A simulation study is conducted using 19 building clusters located in Zhuhai, China. The proposed model is compared with a single-bid model and a step-wise bidding model with constant risk preferences. The results show that it better captures building users’ multiple risk preferences under market clearing price uncertainty. Users tend to secure stable returns through responses with minimal comfort loss, while pursuing excess profits via higher bids for responses involving greater comfort sacrifices. Full article
(This article belongs to the Section Building Energy, Physics, Environment, and Systems)
30 pages, 613 KB  
Article
Can the Digital Economy Enable Sustainable Low-Carbon Development of Grain Production? Mechanism Identification and Testing Based on Green Finance
by Xiaodong Xu, Nan Huang, Ting Liang, Jiali Wang and Likun Wang
Sustainability 2026, 18(8), 3884; https://doi.org/10.3390/su18083884 - 14 Apr 2026
Viewed by 242
Abstract
As a vital engine of economic growth, the digital economy can boost agricultural productivity while curbing carbon emissions from grain production, thereby facilitating the green transformation of traditional agriculture and the sustainable development of grain production systems. It serves as a pivotal anchor [...] Read more.
As a vital engine of economic growth, the digital economy can boost agricultural productivity while curbing carbon emissions from grain production, thereby facilitating the green transformation of traditional agriculture and the sustainable development of grain production systems. It serves as a pivotal anchor for achieving China’s dual-carbon strategic goals in the agricultural sector and supporting the long-term sustainability of national grain security. This paper conducts an in-depth analysis of the carbon emission mitigation mechanisms of the digital economy for sustainable agricultural production. Using panel data covering 30 provincial-level regions in China from 2012 to 2021, this study employs and integrates panel regression estimation, mediating effect analysis, and the Spatial Durbin Model (SDM) framework to identify the underlying pathways through which the digital economy affects carbon emissions from grain production and drives low-carbon sustainable transformation of agriculture. The findings reveal the following: (1) The digital economy exerts a significant negative effect on carbon emission intensity in grain production, laying an empirical foundation for digital-enabled sustainable grain production; (2) It indirectly reduces carbon emission intensity by promoting the development of green finance as a mediating channel, unlocking the sustainable empowerment mechanism of green finance for agricultural low-carbon transition; (3) The development of the digital economy presents pronounced spatial spillover effects: improved digital development in one region also lowers grain production carbon emission intensity in neighboring areas, supporting cross-regional coordinated sustainable development of grain production; (4) The carbon-reduction effects of the digital economy exhibit regional heterogeneity, with more significant emission-reduction outcomes observed in eastern and central regions, while such effects are less prominent in western regions, providing a basis for formulating differentiated regional agricultural sustainable development policies. Based on these findings, this paper puts forward a series of targeted policy recommendations, offering theoretical and practical references for the high-quality development of green and low-carbon agriculture and the overall advancement of sustainable agricultural and rural modernization. Full article
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38 pages, 585 KB  
Review
A Unified Information Bottleneck Framework for Multimodal Biomedical Machine Learning
by Liang Dong
Entropy 2026, 28(4), 445; https://doi.org/10.3390/e28040445 - 14 Apr 2026
Viewed by 208
Abstract
Multimodal biomedical machine learning increasingly integrates heterogeneous data sources (including medical imaging, multi-omics profiles, electronic health records, and wearable sensor signals) to support clinical diagnosis, prognosis, and treatment response prediction. Despite strong empirical performance, most existing multimodal systems lack a principled theoretical foundation [...] Read more.
Multimodal biomedical machine learning increasingly integrates heterogeneous data sources (including medical imaging, multi-omics profiles, electronic health records, and wearable sensor signals) to support clinical diagnosis, prognosis, and treatment response prediction. Despite strong empirical performance, most existing multimodal systems lack a principled theoretical foundation for understanding why fusion improves prediction, how information is distributed across modalities, and when models can be trusted under incomplete or shifting data. This paper develops a unified information-theoretic framework that formalizes multimodal biomedical learning as an information optimization problem. We formulate multimodal representation learning through the information bottleneck principle, deriving a variational objective that balances predictive sufficiency against informational compression in an architecture-agnostic manner. Building on this foundation, we introduce information-theoretic tools for decomposing modality contributions via conditional mutual information, quantifying redundancy and synergy, and diagnosing fusion collapse. We further show that robustness to missing modalities can be cast as an information consistency problem and extend the framework to longitudinal disease modeling through transfer entropy and sequential information bottleneck objectives. Applications to multimodal foundation models, uncertainty quantification, calibration, and out-of-distribution detection are developed. Empirical case studies across three biomedical datasets (TCGA breast cancer multi-omics, TCGA glioma clinical-plus-molecular data, and OASIS-2 longitudinal Alzheimer’s data) show that the framework’s key quantities are computable and interpretable on real data: MI decomposition identifies modality dominance and redundancy; the VMIB traces a compression–prediction tradeoff in the information plane; entropy-based selective prediction raises accuracy from 0.787 to 0.939 at 50% coverage; transfer entropy reveals stage-dependent modality influence in disease progression; and pretraining/adaptation diagnostics distinguish efficient from wasteful fine-tuning strategies. Together, these results develop entropy and mutual information as organizing principles for the design, analysis, and evaluation of multimodal biomedical AI systems. Full article
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23 pages, 1769 KB  
Article
Impact of Transport Infrastructure on Regional Economic Synergy: Evidence from Chinese Cities
by Ruibo Jia, Deqing Wang and Xindi Mou
Sustainability 2026, 18(8), 3855; https://doi.org/10.3390/su18083855 - 14 Apr 2026
Viewed by 365
Abstract
Transport infrastructure serves as a critical physical carrier for constructing a unified national market and promoting coordinated regional economic development. Addressing the practical contradiction between rapid transport network expansion and persistent regional development imbalances, this paper constructs a comprehensive transport infrastructure service efficiency [...] Read more.
Transport infrastructure serves as a critical physical carrier for constructing a unified national market and promoting coordinated regional economic development. Addressing the practical contradiction between rapid transport network expansion and persistent regional development imbalances, this paper constructs a comprehensive transport infrastructure service efficiency index using panel data from 297 prefecture-level cities in China from 2010 to 2023. We systematically investigate the nonlinear impact and underlying mechanisms of transport infrastructure on inter-city economic disparities. The findings reveal a significant inverted U-shaped relationship between transport infrastructure construction and regional economic disparity. Specifically, in the early stages of transport development, the dominance of the agglomeration effect leads to widening regional gaps; once a specific threshold is crossed (an index value of approximately 0.274), the diffusion effect emerges, facilitating convergence. This nonlinear relationship exhibits significant regional heterogeneity: the eastern region has largely crossed the inflection point into the convergence phase, while the western region remains in the “climbing” period dominated by polarization effects. Mechanism testing indicates that labor factor allocation is the core driver of this inverted U-shaped evolution. This study not only clarifies the dynamic boundaries of transport infrastructure’s impact on regional economic patterns but also provides empirical evidence for formulating differentiated transport and regional coordination policies for regions at different developmental stages. Full article
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42 pages, 3396 KB  
Article
A Fuzzy Parametric Entropy-Based TOPSIS Method for Soil Stabilization Suitability Ranking
by Gökhan Çuvalcıoğlu, Sinem Yılmaz Tarsuslu and Arif Bal
Appl. Sci. 2026, 16(8), 3781; https://doi.org/10.3390/app16083781 - 13 Apr 2026
Viewed by 134
Abstract
This study investigates the challenging task of predicting the strength of subgrade soils, which serve as the foundation of superstructure systems. Due to the inherent complexity of soil behavior, traditional empirical methods often fall short in providing consistent and reliable estimations. To address [...] Read more.
This study investigates the challenging task of predicting the strength of subgrade soils, which serve as the foundation of superstructure systems. Due to the inherent complexity of soil behavior, traditional empirical methods often fall short in providing consistent and reliable estimations. To address this limitation, a fuzzy entropy-based TOPSIS multi-criteria decision-making (MCDM) approach is proposed. Methodologically, the study introduces a novel fuzzy entropy function that extends existing fuzzy entropy formulations and is compared against conventional fuzzy entropy measures. Using the newly proposed Pm fuzzy entropy (m = 0.5), a soil stabilization quality ranking was obtained and validated against classical fuzzy entropy-based TOPSIS results. It is important to emphasize that the primary objective of the proposed framework is not to provide direct numerical estimates of CBR values, but rather to support the decision-making process by ranking soil options based on multiple criteria under conditions of uncertainty. The robustness of the rankings was further examined using California Bearing Ratio (CBR) data and comprehensive sensitivity analyses to consider uncertainties from expert judgments and laboratory measurements. The proposed approach offers a solution for multi-criteria decision-making processes in uncertain environments, ensuring high rating consistency and adaptability. Full article
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