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Quantization of geometric-like coupling in gravitational field based on characterization and transformation

Scientific Reports Chen Yang Jul 02, 2026 DOI: 10.1038/s41598-026-53091-5

Abstract Connections between the formulations of physics and geometry have been evident throughout history, from classical mechanics to general relativity. Independently, quantum mechanics has been established in flat space. In this study, we investigate the geometric-like coupling of a test particle and its quantized form in a gravitational field. The main text consists of three parts: the characterization of the particle and its operator form is pointwise established. Minimal coupling with the electromagnetic potential is analyzed as a reference via an infinitesimal transform. Subsequently, the geometric coupling from the geodesic strain and its associated phase transform of the initial parallel test particle is formally studied. Within the gravitational field equation, the phase transform is specified via metric tensors in general. The linearized field condition is analyzed explicitly to show the local analogy between the four-potential in gauge-like and geometric-like couplings. From the isomorphism and function maps, the amplitude and phase in the operator form are translated to the quantum form and the Schrödinger-like equation is obtained. The representation of local equivalence and the phase transform condition is formulated. Examples of the phase shift and potential well, as well as the geometric Aharonov–Bohm effect, are studied for potential applications. Finally, the geometric-like and gauge-like couplings are summarized based on the concept of pointwise characterization and associated matrix transformation.

Epitranscriptomic m6A reader HNRNPC amplifies oxidative stress–autophagy dysregulation and aggravates placental dysfunction in preeclampsia

Scientific Reports Jianli Wu, Li Wang, Ru Yang et al. Jul 02, 2026 DOI: 10.1038/s41598-026-60074-z

A multi-dimensional urban spatial perception framework for urban diagnosis in Wuhan driven by multi-source data

Scientific Reports Xinrui Liu, Ruiying Zhang, Xiang Liu et al. Jul 02, 2026 DOI: 10.1038/s41598-026-60477-y

Aerosols and hydrocarbons in the atmosphere of a white dwarf planet

Nature Ryan J. MacDonald, Christopher E. O’Connor, Victoria A. Boehm et al. Jul 02, 2026 DOI: 10.1038/s41586-026-10514-7

Abstract Most stars, including our Sun, will one day evolve into red giants and, subsequently, white dwarfs. Several planet candidates have recently been identified orbiting white dwarfs 1–4 , demonstrating that planets can survive the stellar post-main-sequence stage intact. Little is known about the atmospheric composition of post-main-sequence planets, with the most evolved transiting planets with atmospheric detections so far orbiting subgiants 5,6 . Here we report an atmospheric detection for the white dwarf planet WD 1856 b, achieved through transmission spectroscopy with the James Webb Space Telescope (JWST) Near-Infrared Spectrograph (NIRSpec) PRISM. Our 0.5–5.0-μm spectrum reveals the presence of hydrocarbons (odds ratio of 167:1–5,377:1, with CH 4 preferred at 17:1–30:1), aerosols (2 × 10 5 :1–2 × 10 6 :1) and thermal emission from the planetary nightside (2 × 10 63 :1–2 × 10 73 :1). Our spectral analysis constrains the mass of WD 1856 b to 4.3–10.9  M J , finds a carbon-enriched atmosphere (with a CH 4 abundance of approximately 7%) and an effective temperature exceeding the expected planetary equilibrium temperature (390–412 K versus 160 K). On the basis of cooling models, these results indicate that WD 1856 b underwent a migration-related reheating event 3.0–5.5 Gyr into the white dwarf phase, consistent with post-main-sequence tidal evolution to the present-day 0.02- au circular orbit. Our results provide a window into the ultimate fate of giant planets orbiting stars with masses similar to our Sun.

LH stimulates a rapid cAMP-mediated, gap junction-dependent activation of PDE3A in oocytes

Scientific Reports Eran Gershon, Iris Maimon, Michal Elbaz et al. Jul 02, 2026 DOI: 10.1038/s41598-026-59161-y

LiteDriveNet for driver distraction classification using a lightweight multi-scale convolutional neural network

Scientific Reports Abirami Namachivayam, Nirmala Paramanandham Jul 02, 2026 DOI: 10.1038/s41598-026-58307-2

Comparison of Mosquito-Magnet trap and livestock-aspirated collection of mosquitoes and the implications for modelling mosquito-borne animal diseases

Scientific Reports Armin R. W. Elbers, Rody Blom, Jose L. Gonzales Jul 02, 2026 DOI: 10.1038/s41598-026-60097-6

Automated tracking of the brown algal parasite Eurychasma dicksonii with deep learning

Scientific Reports Behnoud Shafiezadeh Kenari, Shayan Alvansazyazdi, Davide Cangelosi et al. Jul 02, 2026 DOI: 10.1038/s41598-026-58239-x

Harmonizing standards and resources for the medical genome

Nature Euan A. Ashley, Ash A. Alizadeh, Hanae Armitage et al. Jul 02, 2026 DOI: 10.1038/s41586-026-10621-5

A TabNet-SHAP framework with stability-weighted multi-method feature selection for muscle injury prediction in professional football

Scientific Reports Wenbo Rao Jul 02, 2026 DOI: 10.1038/s41598-026-54749-w

Abstract Muscle injuries account for approximately 31% of all time-loss injuries in professional football, yet existing prediction models are constrained by small sample sizes, dependence on proprietary physiological data, limited interpretability, and inadequate temporal validation designs. This study develops an interpretable, strictly prospective prediction framework trained on 438,219 player-season records sourced from Transfermarkt, spanning 15 seasons (2010/11–2024/25) across 32 leagues. To ensure temporal integrity, all predictive features are constructed exclusively from prior-season data, and models are evaluated under a chronological hold-out design in which earlier seasons serve as training data and the two most recent seasons constitute the test set. We propose a multi-method stability-weighted feature selection (MSFS) strategy that cascades filter-based redundancy removal, four-method ensemble voting, and cross-validation stability verification, reducing 57 candidate features to a robust subset. Under cost-sensitive learning designed for severe class imbalance (6.2% positive rate), TabNet attains the highest discrimination among five candidate classifiers with an area under the receiver operating characteristic curve (AUC) of 0.812 (95% CI: 0.804–0.820), outperforming XGBoost (0.806), LightGBM (0.803), long short-term memory network (LSTM) (0.789), and logistic regression (0.761). Ablation experiments confirm that stability-verified feature selection and metaheuristic hyperparameter optimisation yield complementary performance gains, and direct comparison with Bayesian optimisation demonstrates that the detective behaviour algorithm provides competitive tuning across architectures. A seven-layer Shapley additive explanations (SHAP) interpretability analysis reveals that under the prospective design, injury history emerges as the most important feature category (33%), surpassing market-and-career features (29%), confirming that the temporal correction elevates genuine recurrence risk over reporting-related proxies. A two-stage risk architecture is identified in which market-and-career features establish a baseline risk stratum, whereas historical injury burden acts as a multiplicative amplifier among predisposed individuals. Individual-level decompositions further indicate that substitution-based rotation patterns are associated with attenuated age-related risk elevation. Sensitivity analyses excluding market value features quantify the extent to which predictive performance reflects genuine injury risk versus differential reporting completeness across leagues. These findings demonstrate that publicly accessible transfer-market data, combined with attention-based deep tabular learning and rigorous temporal validation, can support meaningful and interpretable injury risk stratification without proprietary monitoring systems.

Snoring classification with deep time-frequency features

Scientific Reports Wenting Lu, Jibo Han, Weiwei Lei et al. Jul 02, 2026 DOI: 10.1038/s41598-026-58941-w

Reliability of transversus abdominis and gluteus medius muscle thickness measurements using ultrasound imaging in chronic non-specific low back pain individuals

Scientific Reports Thanawat Yodthee, Patraporn Sitilertpisan, Aatit Paungmali et al. Jul 02, 2026 DOI: 10.1038/s41598-026-59099-1

The complex truth about trust in science

Nature Jul 02, 2026 DOI: 10.1038/d41586-026-01974-y

Topology-oriented energy management systems based on supercapacitor charge sustaining and multi-port DC–DC converters for hybrid electric motorcycles

Scientific Reports Hamed Abdi, Hadi Aghaei, Naghi Rostami et al. Jul 02, 2026 DOI: 10.1038/s41598-026-59489-5

An EEG-based hybrid machine learning approach for CT scan triage in mild traumatic brain injury

Scientific Reports Deepika Nelavagal Sridhara, K. S. Hareesha, Ajay Hegde et al. Jul 02, 2026 DOI: 10.1038/s41598-026-60399-9

Abstract Mild traumatic brain injury (mTBI) frequently prompts computed tomography (CT) imaging in emergency departments, despite a high proportion of negative findings. Objective, non-invasive tools that can support CT triage decisions under realistic clinical constraints are therefore needed. This study evaluates whether electroencephalography (EEG)-based biomarkers combined with temporal modeling can provide reliable decision support for mTBI assessment. Resting-state EEG was acquired using a clinically feasible 19-channel montage from 120 subjects classified as CT-Abnormal, CT-Normal, or healthy controls. Automated preprocessing was applied uniformly without manual artifact rejection. Quantitative EEG biomarkers were statistically validated and used to train a Random Forest classifier, while a Long Short-Term Memory (LSTM) network modeled temporal EEG dynamics. The biomarker-based model achieved a test accuracy of 81.25%. A hybrid fusion framework integrating Random Forest and LSTM outputs improved performance, achieving an accuracy of 93.33% and enhanced sensitivity for the CT-Normal category. Generalization was confirmed on an independent test set. These findings indicate that hybrid EEG representations can support CT triage decisions in mTBI as an adjunct to existing clinical assessment.

Scientists should recognize their own political biases to build public trust

Nature Mark Henderson Jul 02, 2026 DOI: 10.1038/d41586-026-01975-x

Optimization of mechanical performance in bioinspired FDM-printed PLA sandwich structures using machine learning

Scientific Reports Sirajudeen Inayathullah, Raviteja Buddala Jul 02, 2026 DOI: 10.1038/s41598-026-55261-x

Child online safety needs more than social-media bans

Nature Kit-Aun Tan Jul 02, 2026 DOI: 10.1038/d41586-026-02068-5

A nationwide cohort study of fracture incidence and postfracture mortality among older adults in Taiwan

Scientific Reports Liang-Yu Chiang, Wei-Yin Kuo, Pei-Syuan Ku et al. Jul 02, 2026 DOI: 10.1038/s41598-026-60581-z

Numerical investigation on the impact of solitary waves with variable incidence angles on offshore box-girder bridges

Scientific Reports Hui Fu, Yunxing Zhang, Chunmei Xie Jul 02, 2026 DOI: 10.1038/s41598-026-60499-6