Restoring frequency in an inverter-dominated microgrid means asking the units for more power. No unit can deliver past its rating, so a careless sharing rule instead pins the smallest ones at full output: no reserve, rising temperature, and eventually the protection that disconnects them, taking capacity from a grid already short—this rating-pinning, not physical output beyond rating (impossible by construction), is what overload means throughout. Published schemes choose their weights by convention, never prove the power split is safe, and say nothing about what happens once demand exceeds capacity. This paper proposes a secondary law that answers all three, and proves it does. Each inverter exchanges one number with its neighbours: its output divided by its own rating. That choice of variable is what makes the guarantees possible, and three follow. Among the classical locally computable degree-based weightings, the one that makes units agree fastest is the harmonic mean of their communication degrees, computed locally; on the test graph it gives 1.82× the connectivity λ2 of Metropolis weights, though after step-size normalisation settling times are similar, so the value is the proof, not the speed. The resulting split is the safest that exists: no other way of delivering the same total power keeps the busiest inverter lighter, so every unit keeps the largest thermal margin available. And once demand exceeds capacity, every unit reaches its limit in finite time and frequency falls at a fixed rate set by the shortfall and system inertia, which says how many seconds remain before load shedding. Eight scenarios, the IEEE 14-bus system, and six published methods on one testbed confirm all of it.
Motorized three-wheeler rickshaws are a major urban transport mode across South Asia, yet their injury-severity patterns remain insufficiently understood. Existing rickshaw safety studies rely largely on structured crash attributes, while narrative-based approaches often treat textual information as a single undifferentiated source. As a result, the distinct roles of contextual conditions, administratively reported crash causes, and crash-event descriptions are rarely preserved within a unified and interpretable prediction framework. To address this gap, this study proposes a mechanism-oriented Distributed Crash Reasoning (DCR) framework for interpretable multiclass injury-severity prediction. DCR preserves three functionally distinct evidence streams: structured contextual conditions, administratively reported crash-cause information, and crash-event descriptions. DCR processes these evidence streams through separate reported-cause, event-interaction, and structured-context modules and integrates them through attention-based multimodal fusion. The framework was evaluated using 2,742 motorized rickshaw crash records from Rawalpindi, Pakistan, covering 2017–2019. The proposed DCR achieved the highest recall, F1-score, and PR-AUC among the evaluated models. Controlled experiments further showed that multimodal structured-text configurations generally outperformed unimodal alternatives. Evidence-stream ablation and faithfulness analyses further identified structured context and crash-event information as the principal predictive sources, while reported-cause information provided a complementary contribution, particularly for Fatal-class discrimination. The multimodal advantage also persisted when models trained on 2017–2018 records were evaluated on 2019 data, indicating later-year predictive consistency within the available dataset. The statistical analysis further identified significant temporal (i.e., weekend, peak period, and nighttime), roadway (i.e., posted speed limit), vehicle (i.e., number of vehicles involved), and human (i.e., driver age and gender) factors, with their associations differing between Severe and Fatal injury outcomes. These findings demonstrate the value of preserving the semantic roles of heterogeneous crash information for class-imbalanced injury-severity prediction while providing diagnostically traceable evidence on the relative roles of different information streams in model predictions.
This work investigates the subject of wormholes with spherical symmetry in a recently proposed curvature-based gravitational framework, namely the & Fouriertrf;(R,Lm,T) theory. This framework has gained much popularity due to its promising feature of direct/indirect matter and curvature interaction. As a first case, we assume the background matter as anisotropic fluid along with a particular wormhole shape model and perform the graphical analysis of the respective energy constraints. This graphical examination is conducted by considering two choices of redshift function: constant and variable radial-dependent forms. Possible constraints on the model parameters are then listed, which refer to the validity of energy bounds. Further, by taking isotropic fluid and a specific EoS parameter as separate cases, the form of the wormhole shape function is computed for both constant and variable redshifts. To comprehend the proposed wormhole geometries, basic axioms regarding wormhole shape models are verified for each case. Further, some crucial measures like complexity factor, total and active gravitational energies, and volume integral quantifier are examined graphically and the 2D as well as 3D embedding visualizations are also provided. Lastly, to reveal the stability of these solutions, we examine the behavior of TOV forces, adiabatic index and speed of sound parameters graphically. It is found that wormhole solution corresponding to isotropic fluid does not satisfy the basic wormhole criteria while the solutions, in other two cases, exhibit valid and physically stable behavior.
Climatic variability threatens crop production in arid and semi-arid regions. This study evaluates the impacts of climatic variability and large-scale teleconnections on Rice and Wheat crops production. Normalized Difference Vegetation Index (NDVI) derived from Landsat data (1994–2023) was used to monitor Crop phenology, precipitation from the Climate Hazards Group InfraRed Precipitation with Station (CHIRPS) and temperature from European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis-5 (ERA5) were used in Random Forest Regression (RFR) model, bias-corrected Coupled Model Intercomparison Project Phase 6 (CMIP6) historical (1994–2014) and future (2021–2100) SSP2-4.5 and SSP5-8.5 scenarios were used to assess projected crop production and teleconnections indices were correlated with crop production. Maximum Rice and Wheat crop cultivated area was 350,000 and 460,000 hectares for Gujranwala and Bahawalnagar respectively. Minimum RMSE was 0.10 and 0.09 hectares for Rice and Wheat crops respectively with CC value of 0.76. Maximum production of Rice and Wheat crops was observed in Gujranwala and Bahawalnagar districts as 650,000 and 1,550,000 (tonnes) with CD of 0.81 and 0.84 respectively using RFR model from 2021 to 2100. The SSP5-8.5 in the period of 2081–2100 showed high temperature ( 29 °C) from 2081 to 2100 in South Punjab and Upper Sindh regions while high precipitation ( 135 mm/month) in Central Punjab region. The significant influence of Atlantic Multidecadal Oscillation (AMO) was observed with the Rice and Wheat crops production in all three regions. Linking teleconnection driven climate anomalies with crop production supports improved agriculture management and climate adaptation strategies in Pakistan.
