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Physics-Informed Neural Networks (PINNs) and Neural Ordinary Differential Equations (NODEs) represent two distinct machine learning frameworks for modeling nonlinear neuronal dynamics. This study systematically evaluates their performance on the two-dimensional Morris-Lecar model across three canonical bifurcation regimes: Hopf, Saddle-Node on Limit Cycle, and homoclinic orbit. Synthetic time-series data are generated via numerical integration under controlled conditions, and training is performed using collocation points for PINNs and adaptive solvers for NODEs (Dormand-Prince method). PINNs incorporate the governing differential equations into the loss function using automatic differentiation, which enforces physical consistency during training. In contrast, NODEs learn the system's vector field directly from data, without prior structural assumptions or inductive bias toward physical laws. Model performance is assessed using standard regression metrics, including Mean Squared Error (MSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and the coefficient of determination. Results indicate that PINNs tend to achieve higher accuracy and robustness in scenarios involving stiffness or sensitive bifurcations, owing to their embedded physical structure. NODEs, while more expressive and flexible, operate as black-box approximators without structural constraints, which can lead to reduced interpretability and stability in these regimes. Although advanced variants of NODEs (e.g., ANODEs, latent NODEs) aim to mitigate such limitations, their performance under stiff dynamics remains an open question. These findings emphasize the trade-offs between physics-informed models, which embed structure and interpretability, and purely data-driven approaches, which prioritize flexibility at the cost of physical consistency.
Education systems worldwide face a growing pressure to align with Sustainable Development Goal 4.7 by embedding Education for Sustainable Development (ESD) into school life. This study examines how primary school headteachers in Cyprus interpret and enact sustainable leadership to advance ESD within a small, highly centralised system. Drawing on sustainable and distributed leadership theories and a whole-school lens, the study employed semi-structured interviews with ten headteachers from diverse regions (urban, rural, and semi-rural). Reflective thematic analysis identified four patterns: (1) leaders sought a strategic integration of ESD into planning and culture; (2) empowerment and participation were pursued through teacher working groups, student eco-councils, and community partnerships; (3) systemic constraints, a rigid curriculum, limited autonomy, and scarce professional development produced a policy–practice gap; and (4) leaders relied on adaptive, collaborative micro-practices to sustain momentum. The findings suggest that, in Cyprus, sustainable leadership operates as a values-based stewardship enacted through ‘quiet activism’. The study highlights implications for leadership development, such as reflexivity, systems thinking, and ethical reasoning, as well as policy design, such as time, autonomy, and structured support for whole-school ESD, in small-state contexts.
Deep learning weather models now match numerical weather prediction accuracy while running orders of magnitude faster, but produce deterministic forecasts without uncertainty estimates, a critical gap for high-stakes decisions during extreme weather events. This paper proposes Neural Tangent Kernel-based uncertainty quantification (NTK-UQ) using last-layer empirical features. Theoretical analysis predicts that UQ quality is architecture-dependent through two mechanisms. First, a variance collapse mechanism explains when UQ fails: when the eigenvalue truncation rank approaches the effective rank of the feature space, the GP correction term consumes nearly all prior variance, destroying discrimination between tropical cyclones and routine conditions; architectures with concentrated spectra (spectral operators) require aggressive truncation (k ≤ 10), while attention-based models tolerate full-rank computation. Second, decomposition performance depends on the non-Gaussian, heavy-tailed structure of extreme weather: Independent Component Analysis exploits higher-order statistics (kurtosis, negentropy) to isolate heavy-tailed extreme-event features, achieving higher discrimination than singular value decomposition, which captures only second-order variance. A data-driven selection rule chooses ICA or SVD from the feature eigenspectrum concentration ratio, correctly prescribing the superior decomposition for all four evaluated architectures. Compared to split conformal prediction (the natural post-hoc baseline), NTK-UQ achieves 31–37% sharper prediction intervals at 90% coverage, and uniquely produces adaptive intervals that scale with extreme event severity, which conformal prediction cannot achieve by construction. The framework requires no retraining; inference-time uncertainty requires only a single matrix-vector product per sample.
School congestion, where student enrollment exceeds school capacity, is a major challenge in low- and middle-income countries. It highly impacts learning outcomes and deepens inequities in education. While subsidy programs that transfer students from public to private schools offer a mechanism to alleviate congestion without capital-intensive construction, they often underperform due to fragmented data systems that hinder effective implementation. The Philippine Educational Service Contracting program, one of the world's largest educational subsidy programs, exemplifies these challenges, falling short of its goal to decongest public schools. This prevents the science-based and data-driven analyses needed to understand what shapes student enrollment flows, particularly how families respond to economic incentives and spatial constraints. We introduce a computational framework for modeling student flow patterns and simulating policy scenarios. By synthesizing heterogeneous government data across nearly 3,000 institutions, we employ a stochastic gravity model estimated via negative binomial regression to derive behavioral elasticities for distance, net tuition cost, and socioeconomic determinants. These elasticities inform a doubly constrained spatial allocation mechanism that simulates student redistribution under varying subsidy amounts while respecting both origin candidate pools and destination slot capacities. We find that geographic proximity constrains school choice four times more strongly than tuition cost and that slot capacity, not subsidy amounts, is the binding constraint. Our work demonstrates that subsidy programs alone cannot resolve systemic overcrowding, and computational modeling can empower education policymakers to make equitable, data-driven decisions by revealing the structural constraints that shape effective resource allocation, even when resources are limited.
In the digital era, balancing digital and nondigital activities is crucial for psychological well-being, underscoring the need for research to enhance health interventions. This study validates the Spanish version of the Digital Life Balance Scale (DLB-Scale) and explores its associations with smartphone addiction scale (SAS), satisfaction with life (SWL), and generalized anxiety disorder (GAD) in a sample of 334 Spanish university students (M = 21.26, SD = 2.23; 72.5% women). The DLB-Scale demonstrated strong internal consistency (Cronbach ' s alpha = 0.87), satisfactory construct validity, and unidimensionality, as confirmed by confirmatory factor analysis (CFI = 0.99, TLI = 0.99, RMSEA = 0.07, SRMR = 0.008 after model adjustment). Strict gender invariance was established, enabling valid cross-gender comparisons. Regression analyses revealed that higher DLB levels were associated with lower SAS (r = -0.426) and GAD (r = -0.182) and greater SWL (r = 0.218). Notably, DLB explained 17.9% of the variance in SAS, compared to 4.5% in SWL and 3.0% in GAD. Additionally, network analysis highlighted DLB as a central construct with strong links to SWL and SAS, corroborating its indirect association with GAD. These findings establish the Spanish DLB-Scale as a reliable tool for assessing digital balance in Spanish-speaking populations. The study offers practical implications for interventions aimed at enhancing DLB to improve well-being and reduce digital stressors.
