Starch fine structure predicts glycemic index variation in whole-grain rice.

We propose a precise and efficient physics-augmented neural network (PANN) to model strain-induced crystallization in rubbery polymers. We demonstrate that the model can be flexibly employed for both unfilled and filled natural rubber (NR). The approach is based on a two potential framework, similar to the concept of generalized standard materials (GSMs). To describe the material behavior, neural network-based free energy and dissipation potentials are employed. The evolution of crystallinity is derived from the two potentials. To ensure boundedness of the crystallinity, a novel constrained GSM-type evolution problem is proposed. To this end, two additional Lagrange multipliers together with the corresponding Karush-Kuhn-Tucker conditions are introduced. As a result, it is guaranteed that crystallinity can be interpreted as a variable of concentration type. The neural network-based potentials ensure all physically desirable properties by construction. Most importantly, objectivity, material symmetry and thermodynamic consistency are automatically fulfilled. In addition, an alternative derivation of the governing model equations in time-discrete form is presented based on an incremental variational framework, which also serves as the basis for a finite element implementation. We demonstrate the predictive capability of the PANN using three different experimental data sets from literature, considering both stress and crystallinity evolution at material point level as well as the corresponding field distributions in a notched specimen. Moreover, we show that model parameterization is also possible when experimental crystallinity data is not available, still enabling suitable stress predictions.

Abstract Gravitational waves provide a unique opportunity to test general relativity in the strong-field regime, enabling the extraction of key physical parameters from observational data. Traditional likelihood-based inference methods, while robust, become computationally expensive in highdimensional parameter spaces, such as when incorporating multiple ringdown modes or beyond Kerr deviations. In this paper, we explore the implementation of a conditional variational autoencoderbased machine-learning framework for accelerated ringdown parameter estimation. As a first application, we use the neural network to infer the remnant properties of a final black hole under the Kerr hypothesis. We demonstrate the performance of this algorithm with simulated ringdown waveforms consistent with advanced LIGO sensitivity and compare with Bayesian analysis results. We further extend the framework beyond the Kerr paradigm by incorporating deviations predicted in braneworld gravity.

In this paper, we investigate the existence of solutions to the following equation: −Δu + (−Δ)su = λ|u|p−2u + μ|u|q−2u in \(\mathbb{R}^N\), where N ≥ 3, λ ≥ 0, μ ≥ 0, μ + λ > 0, 0 < s < 1, and 2∗s ≤ p < q ≤ 2∗. Here, \(2^*_s\) = \(\frac{2N}{N-2s}\) and 2∗ = \(\frac{2N}{N-2}\) denote the fractional and Sobolev critical exponents, respectively. This study fills a theoretical gap in the variational framework for mixed operators by overcoming the loss of compactness caused by critical terms. We analyze three distinct scenarios regarding the parameters p, q, λ, and μ. By combining the mountain pass theorem with Lions’ lemma and the principle of concentration compactness, we establish the existence of a nontrivial solution for each case.

The increasing penetration of photovoltaic (PV) generation requires energy management strategies for PV-battery systems that are not only optimal but also stable and robust under variable solar generation and load demand. Classical optimal control approaches based on first-order optimality conditions ensure stationarity of solutions but provide limited observation into local stability and sensitivity to operational perturbations. This paper introduces a second-order variational framework based on Jacobi equations to analyze and design optimal PV-battery energy management trajectories. The proposed methodology quantifies state-of-charge (SOC) trajectory stability, explicitly identifies conjugate points that signal loss of local optimality, and characterizes time-dependent sensitivity to PV and load fluctuations through Jacobi fields. Numerical experiments on a representative 24-hour PV-battery system demonstrate the practical effectiveness of the approach, revealing critical periods of vulnerability and providing quantitative guidance for battery sizing, control-weight selection, and predictive operational planning. Results show that incorporating second-order optimality conditions enables rigorous stability verification and enhanced robustness compared with classical first-order methods. By extending conventional optimal control frameworks with stability-aware analysis, this work provides a mathematically grounded and practically relevant foundation for resilient energy management in renewable microgrids and residential PV-battery systems.

Bayesian Model Averaging (BMA) enhances predictive performance by integrating over competing models, but its scalability is often limited by the computational burden of Markov chain Monte Carlo (MCMC)–based posterior inference. Recent variational approaches such as VBMA (Kejzlar et al.) offer scalability but rely on restrictive mean-field assumptions that fail to capture posterior dependencies, leading to suboptimal uncertainty quantification in complex settings. We propose Neural Autoregressive Flow Bayesian Model Averaging (NAF-BMA), a novel variational BMA framework that replaces the simple variational family with expressive neural autoregressive flows. This innovation enables NAF-BMA to model highly correlated, multimodal posterior structures with MCMC-level accuracy while retaining near–VBMA scalability. The method jointly estimates individual model evidences and posterior model probabilities within a unified optimization scheme, producing an optimal combined posterior over the entire model space. Designed as a general and modular framework requiring minimal model-specific derivations, NAF-BMA extends naturally to a broad class of Bayesian models. Across extensive simulation and real-data studies, it consistently outperforms VBMA and closely matches MCMC accuracy, establishing NAF-BMA as a flexible and scalable new paradigm for Bayesian model averaging.

The discovery of high-performance multicomponent alloys is constrained by the vastness of composition space and the scarcity of experimentally validated data. We develop VIBANN, a variational information bottleneck-augmented attention-based neural network framework, for uncertainty-aware inverse design of exceptionally hard bulk multicomponent metallic glasses. The model learns chemically structured latent representations of alloy composition and indentation load to search the candidate space under constraints of chemical plausibility, novelty, and predictive uncertainty. Guided by this framework, we synthesize five B-Nb-Fe-W-Co/Hf/Ru/Zr-rich bulk multicomponent metallic glasses. All alloys form fully amorphous rods of 2 mm diameter and reach Vickers hardness values of about 2450 HV, among the highest reported for bulk metallic glasses under comparable conditions. Latent space analysis, attribution trends, and molecular dynamics-based atomistic simulations show that exceptional hardness in this compositional space arises from dense atomic packing, boron-enriched short-range environments and refractory-stabilized local rigidity. Together, we show that uncertainty-aware latent space learning can discover bulk metallic glasses that combine amorphous structure with exceptionally high hardness under limited data conditions.

Quantum computing has emerged as a promising paradigm for tackling electronic structure problems, with most efforts to date focused on molecular energies and, more recently, first-order derivatives. However, the extension to second-order energy derivatives with respect to nuclear coordinates─essential for predicting vibrational spectra and identifying transition states─has remained relatively limited. Here, we present an analytic implementation for computing nuclear Hessians within the variational quantum eigensolver framework. Our approach produces harmonic vibrational frequencies and normal modes in excellent agreement with full configuration interaction (FCI) benchmarks, even for systems with challenging cases of orbital degeneracy or involving weak intermolecular interactions. We further assess the quantum measurement cost of these second-order derivative calculations and compare it with that of variational quantum eigensolver (VQE) energy calculations. Additionally, we demonstrate how point group symmetry can be incorporated to reduce measurement cost without loss of accuracy. This work extends quantum computing capabilities toward advanced quantum chemical simulations, such as the characterization of noncovalent interactions via low-frequency vibrational signatures and the identification of transition states.

We propose a mean quadratic variation (MQV) framework for portfolio selection as an alternative to the classical Markowitz mean–variance (MV) paradigm. Instead of measuring risk by terminal return variance, the MQV framework employs quadratic variation, a pathwise and time-additive measure of return fluctuations. This modification addresses two longstanding limitations of the MV framework: the sensitivity of covariance-based optimization in high-dimensional settings and the time-inconsistency of multi-period portfolio choice. The proposed model is straightforward to calibrate, as quadratic variation and quadratic covariation between assets can be directly estimated from realized return paths. Moreover, the additive structure of quadratic variation yields time-consistent optimal portfolio strategies in a discrete-time multi-period setting. We derive closed-form optimal portfolio weights, characterize the corresponding efficient frontier, and develop a quadratic variation-based capital asset pricing model. Extensive empirical backtests and simulation experiments show that MQV portfolios achieve competitive or improved out-of-sample performance relative to their MV counterparts across several asset universes. Overall, the results suggest that pathwise risk measurement provides a tractable and economically meaningful alternative to variance-based portfolio optimization.

A geometrically exact, dimensionally reduced model is developed to describe the nonlinear deformation of thin magnetoelastic shells. The classical Kirchhoff–Love assumptions for the mechanical fields are extended to the magnetic variables, yielding a consistent two-dimensional theory derived rigorously through a variational framework. Unlike traditional approaches that rely on mid-surface kinematics, the full deformation map is adopted as the primary variable, and the influence of the surrounding free space due to the Maxwell stress on the shell’s upper and lower surfaces is accommodated through a novel application of Green’s theorem. The governing equations are solved in closed form for the canonical case of a hyperelastic thin flat plate and for an infinite cylindrical magnetoelastic shell, to illustrate the capabilities of the model and elucidate the non-standard variables arising in the modified variational formulation.

The ultimate goal of residency education is to train physicians to deliver high-quality patient care. However, residents rarely receive data-driven feedback because resident-level quality measures are lacking. To develop and evaluate resident-sensitive quality measures (RSQMs) using electronic health record data to inform graduate medical education. This cohort study used call schedules linking senior internal medicine residents to patient admissions during overnight internal medicine call shifts at 5 teaching hospitals in Canada from July 1, 2010, through December 31, 2019. Using clinical practice guidelines, 7 RSQMs related to pneumonia or general care for all internal medicine admissions were developed. To support interpretation, a care variation framework was applied that categorized measures as low value (not recommended), discretionary (context dependent), or evidence based (recommended) to enable comparisons between observed and expected variation. The data were analyzed between March 1, 2024, and February 23, 2026. The low-value care RSQM measured potentially inappropriate red cell transfusions (all admissions). Discretionary RSQMs measured use of antibiotics, imaging, or blood work for either pneumonia or all admissions. The evidence-based care RSQM measured ordering of first-line antibiotics for pneumonia. Resident-level variation was assessed using descriptive statistics, including the median proportion of eligible admissions with each RSQM performed and interquartile range. The cohort included 132 291 patient admissions (median [IQR] age, 70 [55-83] years; 50.6% male) linked to 793 residents. Residents had a median (IQR) of 187 (89-228) admissions, including a median (IQR) of 18 (10-24) admissions for pneumonia. Potentially inappropriate red cell transfusions occurred in a low proportion of encounters, with little variation (median, 0%; IQR, 0%-0%). Discretionary measures, including use of second-line antibiotics, advanced imaging, chest computed tomography, and serum protein electrophoresis, varied across residents. For pneumonia admissions (n = 13 470), the RSQM for first-line antibiotic use in pneumonia was sensitive to the time windows for included orders, ranging from 22% (3027 admissions) to 76% (10 205 admissions), depending on the cutoffs applied. This cohort study outlined an approach to developing and evaluating RSQMs using readily available electronic health record data to evaluate internal medicine residents' quality of care. Although the RSQMs showed potential, their use for inpatient internal medicine may be more appropriate at the program level due to unresolved concerns regarding attribution and statistical reliability.

A multi-channel attention-based variational autoencoder framework for incipient fault detection of rolling bearings

The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale simulations. Emerging machine learning-based methods provide data-driven solutions to PDEs, yet they present challenges, including high training cost and low model reusability. Here we propose the neural-operator element method (NOEM) by synergistically combining FEM with operator learning to address these challenges. NOEM leverages neural operators to simulate subdomains that require fine meshes in FEM. In each subdomain, a neural operator is used to build a single element, namely, a neural-operator element (NOE). NOEs are then integrated with standard finite elements to represent the entire solution through the variational framework. Thereby, NOEM does not necessitate dense meshing and offers efficient simulations. We demonstrate the accuracy, efficiency and scalability of NOEM by performing systematic theoretical analysis and numerical experiments, such as nonlinear PDEs, multiscale problems, PDEs on complex geometries and discontinuous coefficient fields.

We formulate and analyze a regularized variational model in which finitely many discrete anchors constrain a scalar field on a bounded Lipschitz domain and, through second-order response, determine a tensorial object of metric type. The analytic point of departure is that singular pointwise anchoring is incompatible with the natural Sobolev setting of the Dirichlet energy. To overcome this difficulty, each anchor is represented by a mollified averaging functional, so that the full anchor mechanism becomes continuous on the admissible class and remains compatible with weak convergence. The resulting action consists of a Dirichlet term, a weighted anchor-fidelity term, and an auxiliary regularization term. Within this framework we derive the first variation, the weak Euler--Lagrange equation, and the second variation in complete form. We then prove existence of minimizers under standard coercivity and weak lower-semicontinuity hypotheses, establish uniqueness under strict convexity, and show that the second-order response is symmetric and positive semidefinite when the regularization is convex. In the quadratic regularization case we obtain a linear elliptic field equation with smooth localized forcing and record the corresponding interior regularity consequences. The geometric conclusion of the paper is stated at its natural level of generality: whenever the second-order response admits a local tensor representation and satisfies an explicit nondegeneracy condition relative to a positive definite reference tensor, it induces a continuous metric-type tensor on the region under consideration. A finite-difference discretization of the quadratic model is also constructed, validated by a manufactured-solution experiment, and used to study the dependence of the reconstructed response tensor on the anchor-fidelity and anchor-width parameters. The paper therefore provides a mathematically controlled Euclidean variational framework in which localized discrete data determine a field and, under explicit hypotheses, a geometric response of metric type.

SUMMARYThis protocol describes a computational approach for constructing correlation-based molecular networks from untargeted metabolomics data using MetVAE, a variational autoencoder-based framework. Complementing spectral similarity networks, it captures functional relationships reflected in cross-sample correlations. The workflow imports metabolomics features and sample metadata, adjusts for compositionality, missingness, confounding, and high-dimensionality, estimates sparse metabolite correlations, and exports GraphML files for network visualization. In a hepatocellular carcinoma mouse model, it links lipid classes in high-fat-diet animals, suggesting an endogenous “auto-brewery” route to lipotoxic metabolites.

Emissions Trading Scheme (ETS) pilot programs impose binding quota constraints and enable allowance trading, reshaping cost structures and strategic interactions in oligopolistic agri-food supply chains. This paper quantifies the resulting economic impacts, including equilibrium prices, profits, and trade flows, by developing a multi-tier network equilibrium model that links upstream suppliers, downstream manufacturers, domestic and international demand markets, and a carbon trading center under an Emissions Trading Scheme pilot setting. Suppliers invest in low-carbon technologies, while manufacturers undertake labor-efficiency investments that affect unit costs and throughput, with proximity-based spillovers captured via a grid-distance mechanism. The equilibrium conditions are formulated as a variational inequality framework and computed numerically, enabling systematic comparative statics analysis under alternative quota stringency and trading conditions. Using China-EU garlic trade as an illustrative case, the numerical analysis indicates that tighter policy constraints and trading conditions shift production and allowance-trading patterns, with corresponding changes in prices, profits, and emissions across tiers. It also shows that moderate efficiency investment can improve productivity and may reduce aggregate emissions, whereas very high unilateral investment tends to exhibit diminishing returns and can be associated with non-smooth adjustments in network allocations. Finally, coordinated upstream-downstream investment is generally associated with more stable outcomes than isolated initiatives. The framework offers a decision-relevant tool for evaluating Emissions Trading Scheme pilot designs in regulated international agri-food trade networks.

The weak-field, quasi-static regime of gravity is commonly described by the Newton-Poisson equation as an effective response law. We construct this response within a cost-first discrete variational framework. The Recognition Composition Law (RCL) uniquely selects a reciprocal closure cost within the restricted quadratic symmetric composition class; together with the discrete ledger axioms AX1-AX5 (including conservation) and standard DEC refinement, the Newton-Poisson baseline is then recovered in the instantaneous-closure limit. Conditional on Assumption AS1 (scale-free latency) and Assumption AS2 (causal frequency-wavenumber ansatz), allowing finite equilibration introduces fractional memory into the response, yielding a scale-free modification of the source-potential relation characterized by a power-law kernel wker(k)=1+C(k0/k)α in Fourier space. The kernel exponent α=12(1-φ-1)≈0.191, where φ=(1+5)/2, is derived from self-similarity of the discrete ledger closure; the amplitude C=φ-2≈0.382 is identified as a hypothesis from a three-channel factorization argument. We evaluate this quasi-static kernel-motivated response against SPARC galaxy rotation curves under a strict global-only protocol (fixed M/L=1, no per-galaxy tuning, conservative σtot), using a controlled multiplicative surrogate for the full nonlocal disk operator implied by the kernel. In this deliberately over-constrained setting, the surrogate interface achieves median(χ2/N)=3.06 over 147 galaxies (2933 points), outperforming a strict global-only NFW benchmark and remaining less efficient than MOND under identical constraints. The analysis is restricted to the non-relativistic, quasi-static sector and should be read as a falsifier-oriented galactic-regime consistency check of the scaling window, not as a relativistic completion or a claim of Solar System viability without additional UV regularization/screening.

Understanding the interplay between electronic correlations and band topology remains a central challenge in condensed matter physics, primarily hindered by a language-mismatch problem. While band topology is naturally formulated within a single-particle band theory, strong correlations typically elude such an effective one-body description. In this work, we bridge this gap by leveraging the ghost Gutzwiller (gGut) variational embedding framework, which introduces auxiliary quasiparticle degrees of freedom to recover an effective band-structure description of strongly correlated systems. This approach enables an interpretable and computationally efficient treatment of correlated topological phases, resulting in energy- and momentum-resolved topological features that are directly comparable to experimental spectra. We exemplify the advantages of this framework through a detailed study of the interacting Bernevig-Hughes-Zhang model. Not only does the gGut description reproduce established results, but it also reveals previously inaccessible aspects: most notably, the emergence of topologically nontrivial Hubbard bands hosting their own edge states, as well as possible ways to manipulate these through a finite magnetization. These results position the gGut framework as a promising tool for the predictive modeling of correlated topological materials.

We develop structure-preserving variational integrators for non-autonomous Lagrangian systems by extending the prolongation–collocation variational integrator framework to explicitly time-dependent dynamics. The proposed method is obtained by discretizing Hamilton’s principle for non-autonomous Lagrangians, leading to a family of discrete Lagrangian functions defined at a fixed time step. By combining Hermite interpolation, the Euler–Maclaurin quadrature formula, and collocation applied to the Euler–Lagrange equations and their prolongations, the resulting scheme retains key qualitative properties of variational integrators, including a discrete symplectic (or cosymplectic) structure and favorable long-time behavior. We clarify the relationship between the proposed integrator and classical variational integrators for autonomous systems, showing that the method naturally reduces to the standard prolongation–collocation formulation in the time-independent case. Numerical experiments on representative examples illustrate the effectiveness of the approach and demonstrate its advantages over standard integration methods for non-autonomous systems.

Ultrasound images have some limitations, such as low signal-to-noise ratio (SNR), speckle noise, lower dynamic range, blurred boundaries, and shadowing; therefore, ultrasound image registration is an important task for estimating tissue motion and analyzing tissue mechanical properties. In this paper, an effective non-rigid ultrasound image registration method is proposed. By integrating intensity, local phase information, and descriptor matching under a variational framework, we can find and track the non-rigid transformation of each pixel under diffeomorphism between the source and target images based on the warping technique. Experiments using simulation and in vivo ultrasound images of the human carotid artery are conducted to demonstrate the advantages of the proposed algorithm, which will act as an important supplement to current ultrasound image registration.