The variational approach to fracture, particularly through its regularization as a phase-field model, has become a widely used tool for simulating the quasi-static propagation of cracks in structures. However, classic incremental loading can induce unstable crack growth, violating the quasi-static assumption, and in some cases, leads to a loss of force balance, preventing self-consistency and the estimation of dissipated energy during snapback instabilities. To address this challenge, path-following methods are investigated. Their aim is to adjust the applied load so that it stays at the propagation threshold, thereby preserving the quasi-static assumption and ensuring equilibrium solutions. In this work, we apply and evaluate multiple path-following methods within the framework of variational phase-field fracture models, which are developed to regularize linear elastic variational sharp crack evolution problems. Our study pursues two objectives. First, we review several existing path-following methods, with a focus on partitioned strategies based on the displacement field, which decouple the path-following control equation from the rest of the system, facilitating easier integration with staggered solvers. In addition, we introduce a new path-following method whose particularity is to limit the maximum strain increment outside the cracked regions. Second, we use the Γ -convergence to the sharp crack model to evaluate these methods across three crack propagation problems of increasing complexity. The comparison demonstrates that the proposed path-following method offers a simple yet highly effective approach to capture the equilibrium path in phase-field fracture simulations. This method robustly maintains the quasi-static assumption, ensuring physically meaningful results. By enabling accurate estimation of the energy dissipated during snapback instabilities, it paves the way for the rational design of more resistant heterogeneous materials. • Identification of generic path-following methods compatible with staggered solvers. • A new method based on the strain outside the cracked zone offers improved performance. • Evaluation by testing the Γ -convergence to sharp crack model through examples of increasing complexity. • Toward numerically robust, self-consistent evaluation of equilibrium crack propagation paths. • Toward rational design of microstructures for enhanced fracture toughness.

Physics-informed sequential data augmentation for three-phase flow modeling

A variational phase-field model for anisotropic fracture accounting for multiple cohesive lengths

Mesh-type reference computational phantoms (MRCPs) for the next general recommendations.

Intratumor heterogeneity (ITH) impacts cancer progression, and its characterization is crucial. Clustering algorithms applied to the variant allele frequency (VAF) of mutations can facilitate the exploratory analysis of ITH. This study comparatively evaluated six clustering algorithms to characterize ITH by clustering mutations based on their VAFs. We utilized data from The Cancer Genome Atlas to analyze three cancer types by examining the distribution of clusters in the results from various methods and four internal validation metrics. The results indicated that the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and Variational Bayesian Gaussian Mixture Model methods identified an insufficient number of clusters in most tumor samples. The Hierarchical DBSCAN (HDBSCAN) and Ordering Points to Identify the Clustering Structure (OPTICS) algorithms exhibited greater variability in the number of clusters, while Affinity Propagation (AP) showed controlled behavior, and Mean-Shift demonstrated greater consistency. The Mean-Shift and AP methods were consistently superior in the validation metrics, in contrast to HDBSCAN and OPTICS, which had inferior performance. We conclude that Mean-Shift and AP are promising and accessible alternatives for the initial exploratory analysis of ITH by VAFs. A computational pipeline is provided on the Google Colab platform to facilitate future studies.

In this study, a variational model is proposed for filtering additive and multiplicative noise in wrapped phase maps. The model includes the Pythagorean identity, which is a fundamental requirement for phase maps, as well as the total variation regularizer to maintain discontinuities. We prove that our model is well-posed, compute the Euler-Lagrange equations, and present a fixed-point convergent algorithm for solving it. The quality of the proposed model is confirmed by conducting experiments on both synthetic and real data. Additionally, the implementation of the parallel fixed-point algorithm to accelerate the model's solution is presented. Implementations consist of OpenMP and CUDA execution on a multicore CPU and GPU, respectively. A comparison of the performance of parallel implementations with state-of-the-art methods is presented using synthetic and real data. According to the findings, our parallel implementations achieve speedups of 12x for multi-core CPUs and 125x for GPUs compared to the serial implementation.

The observation of high heritability in most quantitative traits has been a long-standing puzzle. There is a general consensus that simple models of quantitative genetic variation, which are mostly founded on the assumption of mutation-selection balance in a constant environment, have failed to explain high heritability. To make matters worse, the reasons for failure are unknown, leaving little to guide future model developments. Here we revisit this puzzle by taking the canonical Latter-Bulmer (LB) model and relaxing the assumption of perfect environmental stasis. Instead we assume that the trait optimum changes slowly but steadily in a stochastic manner, similar to models used for phylogenetic comparative methods. We show that our model behaves qualitatively differently to its stationary optimum counterpart even though the optimum only changes slowly. This is the result of a feedback between the adaptation rate and selection coefficient fluctuations. The heritability predictions resulting from this feedback are more consistent with observations and also less sensitive to evolutionary parameters than the classical LB model. We derive a simple formula to predict genetic variation in our model which helps to explain some of our counter-intuitive results and which should be useful for understanding the potential influence of fluctuations in future work. Since the feedback driving our results should also occur in more complex models e.g. with multiple traits, we argue that environmental change has been an essential biological ingredient missing in most previous mutation-selection balance models of quantitative trait heritability.

Abstract Variational quantum algorithms (VQAs) have dominated literature as tools for demonstrating quantum utility on near-term quantum hardware, with applications in optimisation, quantum simulation, and machine learning. While researchers have studied how easy VQAs are to train, the effect of quantum noise on the classical optimisation process is still not well understood. Contrary to expectations, we find that twirling, which is commonly used in standard error-mitigation strategies to symmetrise noise, actually degrades performance in the variational setting, whereas preserving biased or non-unital noise can help classical optimisers find better solutions. Analytically, we study a universal quantum regression model and demonstrate that relatively uniform Pauli channels suppress gradient magnitudes and reduce expressivity, making optimisation more difficult. Conversely, asymmetric noise such as amplitude damping or biased Pauli channels introduces directional bias that can be exploited during optimisation. Numerical experiments on a variational eigensolver for the transverse-field Ising model confirm that non-unital noise yields lower-energy states compared to twirled noise. Finally, we show that coherent errors are fully mitigated by re-parameterisation. These findings challenge conventional noise-mitigation strategies and suggest that preserving noise biases may enhance VQA performance.

The interstellar scintillation observed in radio pulsars arises from interference between electromagnetic waves scattered by electron density fluctuations in the turbulent interstellar plasma, providing a critical tool for probing the small-scale structure of the ionized interstellar medium and the pulsar system itself. The primary aim of this work is to study long-term scintillation variations for a bright and nearby pulsar, PSR J0814$+$7429, carried out from September 2013 to September 2023 with the LOw-Frequency ARray (LOFAR) High Band Antennae in the frequency range 120 - 170 MHz. We derived the basic scintillation parameters, scintillation bandwidth (Δν_̊m d), and scintillation timescale (Δτ_̊m d) from the two-dimensional (2D) auto-covariance function of the dynamic spectra that are a 2D matrix of pulse intensity as a function of time and frequency. We present a long-term monitoring study of Δν_̊m d and Δτ_̊m d for PSR J0814$+7429$, which shows a strong annual variation in the time series of the Δτ_̊m d. From our modeling of the annual variations of scintillation velocities, the scattering screen is anisotropic and located at 0.23 kpc from the Earth, likely corresponding to the boundary of the Local Bubble.

Fast extraction of physically relevant information from images using deep neural networks has led to significant advances in fluorescence microscopy and its application to the study of biological systems. For example, the application of deep networks for kernel density (KD) estimation in single-molecule localization microscopy (SMLM) has accelerated super-resolution imaging of densely labeled structures in the cell. However, localization of fluorescent molecules in dense images is a difficult inverse problem with potentially multiple solutions. To model a probability distribution of solutions to this problem, we propose a generative modeling framework for KD estimation in SMLM based on a conditional variational diffusion model (CVDM). In this framework, CVDM is trained to perform localization tasks on low-resolution measurements by modeling a distribution of high-resolution KD estimates. This approach allows us to probe the structure of the distribution on KD estimates and express uncertainty, which is not currently offered by existing deep models for localization microscopy. We demonstrate that this model permits high-fidelity super-resolution, enables the uncertainty estimation of regressed KD estimates, and has important implications for image restoration in single-molecule and super resolution microscopy.

In recent years, the rapid advancement and application of deep learning in medical imaging have demonstrated its effectiveness in reducing physicians’ workload and lowering the risk of misdiagnosis in pathological spine diagnosis. Nevertheless, deep learning–based models for pathological spine diagnosis have not yet matured to the level required for clinical deployment. Several challenges contribute to this limitation. First, the availability of spinal X-ray images for training is limited, and the class distribution of samples is often imbalanced. Second, conventional deep learning models rely on convolutional kernels that primarily capture local features in X-ray images, while overlooking the global morphological characteristics of the spine. To address these issues, we propose ViTST, a Vision Transformer (ViT)–based model with a self-supervised learning task for scoliosis classification. ViTST incorporates a masked strategy–based self-supervised pretext task to mitigate the challenges posed by limited training data and leverages the ViT architecture to capture global structural features of spinal X-ray images. This design enables more effective modeling of inter-regional relationships and variations within the spine. Moreover, by jointly optimizing reconstruction loss and cross-entropy loss, ViTST learns robust image representations even from relatively small datasets. In addition, we introduce a healthcare Internet of Medical Things (IoMT) architecture to enable the practical deployment of ViTST in clinical environments. Through this IoMT platform, clinicians can monitor patients’ conditions in real time and adapt treatment plans dynamically, thereby enhancing clinical decision-making and accelerating patient recovery. Finally, we conducted extensive experiments on a real-world pathological spine image dataset to validate the effectiveness of the proposed model. Experimental results demonstrate that ViTST achieved a Precision of 0.975, an Accuracy of 0.979, and an F1-score of 0.975, confirming its strong potential for application in clinical practice.

Severe load spectrum development for transport aircraft from measured load data: A representative flight method

Innovative Algorithm for Keratoconus Intelligent Grading Using Variational Encoding Bayesian Gaussian Mixture Model

Investigating the physiological and evolutionary consequences of contaminant exposure in wild populations is critical for understanding long-term ecological impacts of anthropogenic change. However, how and why species persist, even thrive, in highly contaminated regions in the absence of humans remains a topic of much debate. We examined the regulatory and genomic impacts of multigenerational chronic radiation exposure to grey wolves (Canis lupus) within the Chornobyl Exclusion Zone. Wolves within the exclusion zone are at an estimated seven times greater density than surrounding preserves, despite lack of physical barriers to dispersal and chronic exposure to elevated radiation dose. Demographic analyses of genetic variation and home range modelling further suggest that ecological factors may support the wolf population within the exclusion zone. Wolves within Chornobyl exhibit altered leukocyte composition and regulatory signatures within the blood transcriptome that support significant alterations to metabolic and immune response pathways, particularly those influential in DNA damage response indicating radiation-induced immune modulation. Selection scans across genes within the blood transcriptome revealed multiple regions of accelerated Chornobyl-specific divergence at loci with known roles in immunity and response to oncogenesis. Together, these data provide evidence that chronic exposure to ionising radiation may be a significant source of ongoing natural selection in an apex predator after a single contamination event, highlighting multigenerational impacts beyond initial exposure. Further, these results highlight the potential contributions of natural selection to species persistence and proliferation in highly contaminated ecosystems.

• existence of barren plateaux is one of the challenges in the practical use of variational quantum classifiers; • a noise-based mechanism that shifts training data during optimization, helping escape barren plateaux, is proposed; • the approach is tested with a variational quantum classifier modeling BET index changes using other indices from Europe and the United States; • simulations use the Pennylane framework. The barren plateaux phenomenon has been identified as a significant challenge for variational quantum algorithms, particularly for classification tasks. In this article, we propose a novel approach to mitigating this problem for variational quantum classifiers during the optimization phase. The noisy optimization mechanism shifts the training data by adding a small amount of uniform noise, thereby inducing changes in the parameters being searched. The effectiveness of the method is evaluated using real financial data, modeling the evolution of the BET index in relation to well-known indices from neighboring Central and Eastern European countries, as well as from Western Europe and the United States. The results demonstrate that this approach significantly improves upon the corresponding baseline quantum classifier and provides results comparable to those of established classical methods.

Categorical variants, or sets of genomic alterations constrained by shared properties, are pervasive across clinical, regulatory, and research domains in the biomedical ecosystem, yet their inconsistent and non-computable representation hinders data interoperability and clinical interpretation. We surveyed genomic knowledgebases spanning regulatory approvals and the biomedical literature and found that categorical variants underpin a substantial proportion of clinical genomics knowledge, but are largely described using incompatible bespoke models. To address this, we developed the GA4GH Categorical Variation Representation Specification (Cat-VRS), a constraint-based framework that provides a unified computable representation for both precise and intentionally broad categories across molecular and systemic variant domains. Cat-VRS enables harmonization of genomic knowledgebases, computable category-based search, and automated matching between assayed variants and categorical entities in clinical and research contexts. By providing a principled, extensible model for categorical variation, Cat-VRS enables computable reasoning over genomic variant categories and establishes a foundation for the standardized representation and exchange of genomic knowledge.

Thermal infrared remote sensing offers a cost-effective means of regional geothermal reconnaissance, yet a fundamental challenge remains: isolating the weak geothermal surface signal (typically 1–3 °C) from dominant surface noise introduced by seasonal temperature cycles (annual amplitude > 20 °C), topographic variability, land cover heterogeneity, and irregular cloud-affected satellite sampling. Conventional single-scene or arithmetic-mean approaches are highly susceptible to these confounding factors and frequently produce pseudo-anomalies that obscure genuine geothermal targets. To overcome this limitation, we propose a physics-based time-series framework in which a nonlinear annual temperature variation model, T(t) = T0 + A·sin(2πt/τ + φ), is fitted to multi-temporal Landsat 8 thermal infrared data via the Levenberg–Marquardt algorithm. Applied to ~50 cloud-free scenes (2021–2022) processed on the Google Earth Engine over the Shanxi Graben System, northern China, the model simultaneously retrieves the background temperature parameter T0 and seasonal amplitude A—two physically interpretable quantities that encode distinct geothermal signatures more robustly than simple temporal statistics. Sub-regional corrections for the elevation (−4 °C/100 m above 800 m), aspect (R2 > 0.95 in piecewise linear segments), and slope further suppress topographic pseudo-anomalies prior to anomaly extraction. Over known high-temperature geothermal fields (Tianzhen and Yanggao; >100 °C at 100 m depth), the method reveals clear T0 offsets of +1–2 °C (3–5% relative) and amplitude deficits of ~2 K (5–10% relative) relative to the background, with model-fitted T0 values averaging ~2 °C higher than arithmetic means due to the correction for seasonal sampling bias. Combined with 5 km fault-proximity buffers, extracted anomaly zones align well spatially with known geothermal sites and major structural corridors of the graben system. However, deeper low-temperature systems (45–50 °C at 300–500 m depth) produce ambiguous signals below the ~1.5 K detection threshold, indicating inherent limitations for deeply buried resources. The fully reproducible, training-data-free workflow is implementable via open satellite archives and cloud computing platforms, making it a transferable low-cost tool for structurally controlled geothermal reconnaissance across extensional basins worldwide.

Quantum machine learning (QML) is rapidly transitioning from theoretical promise to practical relevance across data-intensive scientific domains. In this review, we provide a structured overview of recent advances that bridge foundational quantum learning principles with real-world applications. We survey foundational QML paradigms, including variational quantum algorithms, quantum kernel methods, and neural-network quantum states, with emphasis on their applicability to complex quantum systems. We examine neural-network quantum states as expressive variational models for correlated matter, non-equilibrium dynamics, and open quantum systems, and discuss fundamental challenges associated with training and sampling. Recent advances in quantum-enhanced sampling and diagnostics of learning dynamics, including information-theoretic tools, are reviewed as mechanisms for improving scalability and trainability. The review further highlights application-driven QML frameworks in drug discovery, cancer biology, and agro-climate modeling, where data complexity and constraints motivate hybrid quantum–classical approaches. We conclude with a discussion of federated quantum machine learning as a route to distributed, privacy-preserving quantum learning. Overall, this review presents a unified perspective on the opportunities and limitations of QML for complex systems.

Multi-particle neural operator transformer for solving partial differential equations.

To reveal the regional differentiation characteristics of carbon emissions during the construction phase of expressways and to improve prediction accuracy, six typical expressway projects located in the plain, hilly, and mountainous regions of Anhui Province were selected as case studies. A carbon emission accounting model for the construction phase was established based on the life cycle assessment method, and the effects of the bridge-tunnel ratio, subproject structure, and material and energy consumption on carbon emission intensity were systematically analyzed. On this basis, a regional carbon emission prediction model was developed and optimized using data from 21 completed expressways across the province. The results indicate that carbon emission intensity exhibits a significant topographic gradient, with mountainous regions showing higher values than hilly regions, and hilly regions higher than plain regions. The maximum carbon emission intensity in mountainous projects reaches 5.27 × 10⁷ kg CO₂/km, which is 2.86 times that of plain regions. As terrain complexity increases, the carbon emission structure shifts from being dominated by subgrade engineering and interchange engineering to being dominated by structural engineering, such as bridges and tunnels. In mountainous regions, emissions from structural engineering account for more than 50% of the total emissions. At the material level, cement and steel are identified as the primary emission sources, jointly accounting for 78% of total emissions in mountainous projects, and demonstrating the highest sensitivity to variations in total emissions. The prediction results show that the baseline model using the bridge-tunnel ratio as a single variable achieves a coefficient of determination (R²) of 0.69. After incorporating material and energy consumption variables, the optimized XGBoost model improves the coefficient of determination to 0.9517, achieving high-accuracy prediction using only eight categories of material and energy consumption indicators. Based on the analytical results, differentiated emission reduction pathways are proposed. In mountainous regions, priority should be given to optimizing the design of tunnels and interchange engineering and controlling the intensity of high-carbon structural materials. In plain and hilly regions, emphasis should be placed on low-carbon design and construction optimization of bridge and culvert engineering and subgrade engineering. This study provides a data-driven basis for regional carbon emission prediction and emission reduction decision-making during the construction phase of expressways.