Stochastic gradient optimization is the dominant learning paradigm for a variety of scenarios, from classical supervised learning to modern self-supervised learning. We consider stochastic gradient algorithms for learning problems whose objectives rely on unknown nuisance parameters, and establish non-asymptotic convergence guarantees. Our results show that, while the presence of a nuisance can alter the optimum and upset the optimization trajectory, the classical stochastic gradient algorithm may still converge under appropriate conditions, such as Neyman orthogonality. Moreover, even when Neyman orthogonality is not satisfied, we show that an algorithm variant with approximately orthogonalized updates (with an approximately orthogonalized gradient oracle) may achieve similar convergence rates. Examples from orthogonal statistical learning/double machine learning and causal inference are discussed.

We introduce a novel data-driven symplectic induced-order modeling (ROM) framework for high-dimensional Hamiltonian systems that unifies latent-space discovery and dynamics learning within a single, end-to-end neural architecture. The encoder-decoder is built from Henon neural networks (HenonNets) and may be augmented with linear SGS-reflector layers. This yields an exact symplectic map between full and latent phase spaces. Latent dynamics are advanced by a symplectic flow map implemented as a HenonNet. This unified neural architecture ensures exact preservation of the underlying symplectic structure at the reduced-order level, significantly enhancing the fidelity and long-term stability of the resulting ROM. We validate our method through comprehensive numerical experiments on canonical Hamiltonian systems. The results demonstrate the method's capability for accurate trajectory reconstruction, robust predictive performance beyond the training horizon, and accurate Hamiltonian preservation. These promising outcomes underscore the effectiveness and potential applicability of our symplectic ROM framework for complex dynamical systems across a broad range of scientific and engineering disciplines.

Reliable uncertainty quantification is crucial for trustworthy decision-making and the deployment of AI models in medical imaging. While prior work has explored the ability of neural networks to quantify predictive, epistemic, and aleatoric uncertainties using an information-theoretical approach in synthetic or well defined data settings like natural image classification, its applicability to real life medical diagnosis tasks remains underexplored. In this study, we provide an extensive uncertainty quantification benchmark for multi-label chest X-ray classification using the MIMIC-CXR-JPG dataset. We evaluate 13 uncertainty quantification methods for convolutional (ResNet) and transformer-based (Vision Transformer) architectures across a wide range of tasks. Additionally, we extend Evidential Deep Learning, HetClass NNs, and Deep Deterministic Uncertainty to the multi-label setting. Our analysis provides insights into uncertainty estimation effectiveness and the ability to disentangle epistemic and aleatoric uncertainties, revealing method- and architecture-specific strengths and limitations.

The two-sample testing problem, a fundamental task in statistics and machine learning, seeks to determine whether two sets of samples, drawn from underlying distributions $p$ and $q$, are in fact identically distributed (i.e. whether $p=q$). A popular and intuitive approach is the classifier two-sample test (C2ST), where a classifier is trained to distinguish between samples from $p$ and $q$. Yet despite simplicity of the C2ST, its reliability hinges on access to a near-Bayes-optimal classifier, a requirement that is rarely met and difficult to verify. This raises a major open question: can a weak classifier still be useful for two-sample testing? We show that the answer is a definitive yes. Building on the work of Hu and Lei (2024), we analyze two conformal variants of the C2ST that convert the scores from any trained classifier -- even if weak, biased, or overfit -- into exact, finite-sample p-values. We establish two key theoretical properties of the conformal C2ST: (i) finite-sample Type-I error control, and (ii) non-trivial power that degrades gently in tandem with the error of the trained classifier. The upshot is that even poorly performing classifiers can yield powerful and reliable two-sample tests. This general framework finds a powerful application in Bayesian inference, particularly for validating Neural Posterior Estimation (NPE) models, where the task of comparing a learned posterior approximation $q(θ\mid y)$ to the true posterior $p(θ\mid y)$ can be framed as a two-sample test. Empirically, the Conformal C2ST outperforms classical discriminative tests across a wide range of benchmarks for this task. Our results establish the conformal C2ST as a practical, theoretically grounded diagnostic tool.

Retrieval-Augmented Generation (RAG) has emerged as a critical technique for enhancing large language model (LLM) capabilities. However, practitioners face significant challenges when making RAG deployment decisions. While existing research prioritizes algorithmic innovations, a systematic gap persists in understanding fundamental engineering trade-offs that determine RAG success. We present the first comprehensive study of three universal RAG deployment decisions: whether to deploy RAG, how much information to retrieve, and how to integrate retrieved knowledge effectively. Through systematic experiments across three LLMs and six datasets spanning question answering and code generation tasks, we reveal critical insights: (1) RAG deployment must be highly selective, with variable recall thresholds and failure modes affecting up to 12.6\% of samples even with perfect documents. (2) Optimal retrieval volume exhibits task-dependent behavior QA tasks show universal patterns (5-10 documents optimal) while code generation requires scenario-specific optimization. (3) Knowledge integration effectiveness depends on task and model characteristics, with code generation benefiting significantly from prompting methods while question answering shows minimal improvement. These findings demonstrate that universal RAG strategies prove inadequate. Effective RAG systems require context-aware design decisions based on task characteristics and model capabilities. Our analysis provides evidence-based guidance for practitioners and establishes foundational insights for principled RAG deployment. Our code, data and artifacts are publicly available at https://github.com/ShengmingZ/RAG_Benchmark_Code_QA.

Cybersecurity organizations are adapting to GenAI integration through modified frameworks and hybrid operational processes, with success influenced by existing security maturity, regulatory requirements, and investments in human capital and infrastructure. This qualitative research employs systematic document analysis and comparative case study methodology to examine how 25 studies from 2022 to 2025 document organizational adaptation of threat modeling frameworks, revealing a shift away from traditional signature-based systems toward AI-capable frameworks across three primary patterns: LLM integration for security applications, GenAI frameworks for risk detection and response automation, and AI/ML integration for threat hunting and matching. Organizations with mature infrastructures, particularly in finance and critical infrastructure, demonstrate higher readiness through structured governance, dedicated AI teams, and robust incident response processes, with central banks and financial institutions leading adaptation efforts under regulatory pressure. Successful integration requires human oversight of automated systems, attention to data quality and explainability, and sector-specific governance, though ongoing difficulties with privacy protection, bias reduction, personnel training, and adversarial defense persist. Notable imbalances between offensive and defensive GenAI capabilities create strategic concerns for security planning. The findings offer actionable insights for cybersecurity professionals and underscore the need for adaptive approaches, ethical frameworks, and staff development when managing AI-enhanced threats.

Quantum kernel functions built using quantum-mechanical principles and have emerged as a centerpiece of quantum machine learning. The initial enthusiasm for quantum kernel machines has been tempered by recent studies suggesting that quantum kernels could not offer significant computational or statistical advantages when learning from classical data. However, most of the research in this area has been devoted to scalar-valued kernels in standard classification or regression settings for which classical kernel methods are efficient and effective, leaving very little room for improvement with quantum kernels. In this position paper, we argue that progress in this field requires moving beyond scalar-valued kernels toward more expressive kernel frameworks. Scalar-valued kernels lack the degrees of freedom necessary to fully exploit intrinsically quantum resources such as entanglement and are not rich enough to deal with complex learning tasks where classical learning methods struggle. Building on recent advances in operator-valued kernel learning and $C^*$-algebraic kernel representations, we propose a roadmap for designing quantum kernels capable of leveraging entanglement and non-commutative structures to tackle complex structured prediction problems. To support this viewpoint, we present an initial proof-of-concept illustrating how quantum operator-valued kernel formulations can reveal structural dependencies that remain difficult to access for scalar-valued kernel methods. This shift in focus could open a pathway toward a new generation of quantum kernel machines and a more faithful exploration of their potential advantages.

Modern recommender systems often create information cocoons, restricting users' exposure to diverse content. The central challenge is to balance content exploration and exploitation while allowing users to adjust their recommendation preferences. Ideally, this balance can be captured with a hierarchical representation, where depth search facilitates exploitation and breadth search enables exploration. However, existing approaches face two fundamental limitations: Euclidean methods struggle to capture hierarchical structures, while hyperbolic methods, despite their superior hierarchical modeling, lack semantic understanding of user and item profiles and fail to provide a principled mechanism for balancing exploration and exploitation. To address these challenges, we propose HERec, a hyperbolic framework that effectively balances exploration and exploitation in recommender systems. Our framework introduces two key innovations: (1) a semantic-enhanced hierarchical mechanism that aligns rich textual descriptions with collaborative information directly in hyperbolic space. Theoretical gradient analysis demonstrates that this alignment effectively leverages the underlying hyperbolic manifold structure, resulting in more accurate modeling of users and items; (2) an automatic hierarchical clustering mechanism by optimizing Dasgupta's cost, which discovers hierarchical structures without requiring predefined hyperparameters, enabling user-adjustable exploration-exploitation trade-offs. Extensive experiments demonstrate that HERec consistently outperforms both Euclidean and hyperbolic baselines, achieving up to 5.49% improvement in utility metrics and 11.39% increase in diversity metrics, effectively mitigating information cocoons.

We introduce FLOWR, a novel structure-based framework for the generation and optimization of three-dimensional ligands. FLOWR integrates continuous and categorical flow matching with equivariant optimal transport, enhanced by an efficient protein pocket conditioning. Alongside FLOWR, we present SPINDR, a thoroughly curated dataset comprising ligand-pocket co-crystal complexes specifically designed to address existing data quality issues. Empirical evaluations demonstrate that FLOWR surpasses current state-of-the-art diffusion- and flow-based methods in terms of PoseBusters-validity, pose accuracy, and interaction recovery, while offering a significant inference speedup, achieving up to 70-fold faster performance. In addition, we introduce FLOWR:multi, a highly accurate multi-purpose model allowing for the targeted sampling of novel ligands that adhere to predefined interaction profiles and chemical substructures for fragment-based design without the need of re-training or any re-sampling strategies

Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data. Convergence problems during training are overcome by Wasserstein GANs which minimize the distance between the model and the empirical distribution in terms of a different metric, but thereby introduce a Lipschitz constraint into the optimization problem. A simple way to enforce the Lipschitz constraint on the class of functions, which can be modeled by the neural network, is weight clipping. It was proposed that training can be improved by instead augmenting the loss by a regularization term that penalizes the deviation of the gradient of the critic (as a function of the network's input) from one. We present theoretical arguments why using a weaker regularization term enforcing the Lipschitz constraint is preferable. These arguments are supported by experimental results on toy data sets.

Condensable algebras in 2+1d non-chiral topological orders characterize gapped boundary conditions and interfaces. Applied to the Symmetry Topological Field Theory, they allow classification of symmetric gapped phases and impose sharp constraints on possible phase transitions. A condensable algebra is specified not only by its underlying set of anyons, which end on the boundary or interface, but also by its algebra structure. We introduce the concept of twin condensable algebras, which have the same anyon decomposition, but inequivalent algebra structure. We revisit the classification of condensable algebras in $\mathcal{Z}(\text{Vec}_G^ω)$, i.e. in group-theoretical topological orders for finite groups $G$ with anomaly $ω$. In this context we are able to identify twin algebras that arise from different mechanisms, such as subgroup data, SPT cocycles, and symmetry actions. In particular, we construct infinite families of examples of twins from so-called Gassmann triples, and exhibit cases in which the reduced topological orders are inequivalent despite having identical anyon content. Physically, twin algebras describe distinct symmetric phases that have isomorphic spaces of ground states, but inequivalent order parameters. Such twin phases never exhibit relative spontaneous symmetry breaking, and can be used to construct phase transitions without hidden symmetry breaking, which are intrinsically beyond Landau transitions.

We introduce the concept of twin phases for a symmetry $\mathcal{S}$, defined as inequivalent phases, whose order parameters are part of the same generalized charge under $\mathcal{S}$. Stable, direct transitions between such twin phases are never spontaneous-symmetry-breaking transitions, even after (partially) gauging the initial symmetry $\mathcal{S}$: they are phase transitions without hidden symmetry breaking. We illustrate this with an (anomalous) finite group symmetry in 1+1d, which exhibits such intrinsically beyond Landau transitions.

We present a novel possibility that a network of domain walls bounded by cosmic strings generates a stochastic gravitational wave background (SWGB) signal originating from the spontaneous breaking of a gauged $U(1)_F$ flavor symmetry and the subsequent breaking of discrete $Z_2$ symmetry that accommodates dark matter. The gravitational wave (GW) spectrum produced by the string-bounded-wall network can be detected for high $U(1)_F$ breaking scales in forthcoming GW detectors including LISA, ET and SKA. The GW signal exhibits a distinctive frequency slope, in the infrared, compared to the standard cosmic-string case, in the frequency range between micro-hertz and hertz. We develop a possible strategy to distinguish and characterize GW spectrum of the hybrid defect from from other defects, such as stable cosmic strings, via employing the exact calculation with a machine-learning surrogate, based on a multilayer perceptron (MLP), trained on spectra obtained from the full numerical treatment. This is then used for rapid inference in the detector-specific signal-to-noise ratio (SNR) computation which also makes the process fast and efficient. We also discuss some possible complementarity between GW searches and Flavor observables in the laboratory.

Empirical Bayes analyses routinely model noisy measurements of latent parameters as normal, justifying this by an informal appeal to the central limit theorem (CLT). This paper puts this heuristic appeal on firmer analytical grounds. We show that the denoising regret of the nonparametric maximum likelihood estimator (NPMLE) and related sieve methods is controlled by the rate attained under exact normality, plus a term reflecting the quality of the CLT approximation. The CLT need only hold marginally for each coordinate, and moreover only on average, without needing high-dimensional normal approximations. We identify two asymptotic regimes in which the normal approximation is adequate and the empirical Bayesian prior remains informative, and we show that our guarantees are robust to dependence and to variance estimation.

Floquet engineering offers powerful tools to manipulate quantum states by periodically driving physical parameters. In this work, we investigate the quantum transport through two periodically driven impurities in a mesoscopic one-dimensional channel. By mapping the time-dependent Hamiltonian into an effective multichannel scattering problem, we unveil a rich landscape of transport phenomena arising from the interplay between Fabry-Perot cavity modes and Fano interference. We demonstrate that the inter-impurity distance acts as a critical control parameter, allowing for the formation of Bound States in the Continuum (BICs). Furthermore, we identify Quasi-BICs, extremely narrow resonances with finite lifetimes, that can be dynamically tuned by the drive amplitude. We show that these states enable a robust coherent trapping mechanism, allowing the system to switch from perfect transparency or reflection to strong localization with giant Wigner time delays. Our results suggest possible applications for tunable delay lines and quantum memories, with feasible experimental realizations in the context of cold atoms.

The crucial feature of resurgence theory is the ambiguity of non-perturbative behavior, reflected either in the different choices of integration contours or in the existence of several solutions to Ward identities. This is well illustrated by considering exactly solvable models, of which the prominent example is Chern-Simons theory. Its important chapter, which should have a direct generalization to arbitrary Yang-Mills, is the consideration of Wilson averages in the double-scaling limit of large representation and small coupling. For historical reasons, we call it a Kashaev limit. It possesses a natural interpretation in terms of quasiclassical/WKB approximation, which is, however, somewhat peculiar and thus sheds new light on the old story. The crucial point is the appearance of Alexander polynomials $Δ$ in two seemingly opposite roles: the classical $A$-polynomials have common roots with $Δ$, while Jones polynomials tend to $Δ^{-1}$ in the perturbative expansion. The consistency is provided by the peculiar form of the quantum $A$-polynomial, and the resolution of the puzzle is the co-existence of two different branches (phases) in the quasiclassical limit -- with non-trivial and with vanishing classical actions. The first leads to classical $A$-polynomials and hyperbolic volumes, the second -- to inverse Alexanders.

We consider axisymmetric no-swirl solutions to the three-dimensional incompressible Euler equations, with initial velocity in $C^{1,α}\cap L^2$, where $α\in\left[\frac{1}{3},1\right)$. Motivated by Shkoller's Lagrangian clock-and-driver framework for finite-time blow-up below the $C^{1,\frac{1}{3}}$ threshold, we introduce coherent Lagrangian classes of initial data and conditional solutions for which the same clock mechanism yields a supercritical/critical barrier when $α\geq\frac{1}{3}$, with a genuinely depleted barrier for $α>\frac{1}{3}$ and an exponential bound at the critical endpoint $α=\frac{1}{3}$. In the general case, we formulate a matrix-clock criterion in terms of the smallest singular value of the deformation gradient and show that, under cusp-tail, Dini coherence, near-field compatibility, and bounded transverse-distortion hypotheses, this singular value cannot collapse in finite time. In the on-axis case, the criterion reduces to the scalar clock inequality $\displaystyle \dot{J}(t)\gtrsim -B(t)J(t)-CJ(t)^{3α}$, which rules out Shkoller-type clock collapse for $α\geq\frac{1}{3}$. These results do not enlarge the known Lorentz-space global regularity classes. Rather, they in particular identify the supercritical Lagrangian obstruction dual to Shkoller's subcritical blow-up mechanism in the case $α>\frac{1}{3}$.

We study the global evolution problem for the Einstein equations under T2 symmetry on T3, allowing vacuum, scalar-field, and compressible-fluid matter models, governed by a general equation of state including isothermal and polytropic fluids. Under this symmetry, we obtain the first non-perturbative, global existence and stability theory with connection coefficients being merely square-integrable, which allows both impulsive gravitational waves and shock waves. In areal gauge, we introduce new fluid and geometric variables and reformulate the Einstein-Euler system as a first-order system of nonlinear balance laws with constraints and an entropy structure. The resulting formulation exhibits hyperbolicity, null forms, entropy currents, div-curl structure, maximum principles, and spacetime estimates. This leads to a notion of tame Einstein-Euler flow for which the essential geometric and fluid variables are square-integrable (finite energy), and the secondary variables are absolutely continuous (or, more generally, of bounded variation). In this non-perturbative and weak regularity setting, the equations remain meaningful even when the Weyl curvature concentrates into Dirac masses along timelike hypersurfaces, and the Ricci curvature remains only integrable. Our main results are a global existence theorem for areal foliations, a nonlinear stability theorem for well-prepared initial data, and a nonlinear instability theorem for geometrically oscillatory data, the latter producing measure corrections to the stress energy tensor. In the future-contracting regime, the areal foliation reaches a geometric singularity where the volume of T3 spatial slices degenerates to zero. The areal function reaches zero generically in the non-vacuum Gowdy-symmetric and vacuum torus-symmetric cases. In the future-expanding regime, the areal foliation is complete.

Strongly correlated electrons can be treated with a configuration interaction of Slater determinants grouped by number of unpaired electrons with exponential cost. The first two papers in this series demonstrated that single reference methods built from Richardson-Gaudin states gave results of similar quality at polynomial cost. In this contribution, the states are simplified substantially yielding the perfect-pairing state as a reference along with its low-lying excitations. The states are much simpler, the computational cost is substantially reduced, and there is no sacrifice in numerical accuracy. Second-order Epstein-Nesbet perturbative corrections for the valence electrons are similar in quality to the complete active space self-consistent field.

This paper develops a functional theory for multi-target detection, where a compactly supported signal is recovered from a single noisy observation containing many unknown translations of the signal. Our formulation allows continuous, off-grid translations and correlated stationary Gaussian process noise, extending beyond the discrete, grid-aligned, white-noise models common in prior work. We analyze two uninitialized recovery algorithms based on autocorrelation analysis; in particular, both algorithms first estimate the signal's bispectrum via a debiased third-order empirical autocorrelation. The signal is then recovered from the estimated bispectrum using either a functional frequency marching scheme or a Kotlarski-type deconvolution formula. For both algorithms, we prove non-asymptotic recovery guarantees for compactly supported signals without bandlimiting assumptions. The resulting error bounds depend on the smoothness of the signal and the accuracy of bispectrum estimation, with the latter governed by the noise characteristics and the number of signal occurrences. Numerical experiments validate our theory and demonstrate accurate recovery in low-SNR regimes.

We propose an RG-improved effective-field-theory framework for the deeply bound dibaryon $d^*(2380)$, a $ΔΔ$ bound state in the $(J,I)=(3,0)$ ${}^7S_3$ channel. Its binding momentum $γ\simeq 320$ MeV gives $γ/m_π\simeq 2.3$, indicating the need to re-organize the short-range dynamics beyond a formal pionless EFT. We match the large-$N_c$-constrained pionless contact potential to a meson-exchange-saturated contact interaction in which the $σ,ρ,ω$ dynamics are integrated out at the hadronic scale $m_V$, yielding the controlled expansion parameter $γ/m_V\simeq 0.42$. Normalizing the contact coupling to the deuteron and substituting the phenomenological CD-Bonn couplings gives $B_{ΔΔ}\simeq 96$ MeV. The $\simeq 14\%$ discrepancy from $B_{\rm exp}=84$ MeV is of the natural size of $\mathcal{O}(1/N_c^2)\simeq 11\%$ corrections to the $NN$ potential, confirming compatibility with a controlled EFT expansion organized around the finite-range hadronic scale. As a result, the observed $d^*(2380)$ pole emerges from the virtual state to bound state by using the EFT re-organization in this work.

Radical Moral Disagreements (RMDs) are highly polarising topics that are increasingly censored in everyday life, with growing evidence suggesting that this polarisation carries measurable costs to public mental health. To address these challenges, some researchers have proposed Large Language Models (LLMs) as a means to support more democratic deliberation and better moral reasoning. Yet existing tools are poorly calibrated to help people navigate RMDs, because of their intense and divisive characteristics. This paper introduces CONSIDER, a prototype for a one-to-one AI tool for RMD navigation. Drawing on Mill's account of the epistemic value of disagreement, CONSIDER aims at value clarification through structured disagreement with an opposing LLM-generated opinion. We describe CONSIDER's design logic and analyse potential risks posed by such tools to guide future development.

In this article, a one-off option for temporary service rate control for the M/M/1 queue is considered. After taking this option, during a single exponentially distributed period, two service rates are available for use. Once service rate control is lost, the system continues with a fixed service rate $μ$. The objective is to minimise the sum of holding costs and service costs. We approximate the expected total saved cost by taking the one-off option, depending on the starting state or starting distribution. Using the Value Iteration algorithm with $M$-uniform geometric recurrence, we present methods to approximate the expected total saved future cost, as well as the expected total saved discounted future cost. Furthermore, we obtain theoretical results on the structure of optimal policies and strong Blackwell optimality. The paper is concluded by numerically applying the methods to various instances of the model.

The fully self-consistent $GW$ (sc$GW$) approximation provides a Green's-function approach that is starting-point independent and offers a favorable cost-to-accuracy balance compared to high-level wavefunction methods. Here, we present an all-electron sc$GW$ study of uranium-containing diatomics (UC, UN, UO, and UF), incorporating relativistic effects through the exact two-component (X2C) formalism. We evaluate adiabatic ionization energies as well as electron-attachment and detachment energetics (AEA and VDE), together with equilibrium structures and harmonic vibrational frequencies, and we assess their sensitivity to basis-set choice and relativistic treatment. We find that sc$GW$ yields ionization energies and vibrational properties in very good agreement with experiment and high-accuracy theoretical estimates. For AEA and VDE, diffuse basis sets are essential for convergence. UF is a particularly challenging case for scalar relativistic methods because its electron-attachment and vertical detachment energies are strongly affected by spin--orbit coupling, highlighting the need for a variational two-component treatment. These results establish all-electron X2C-sc$GW$ as a practical route for accurate actinide-molecule energetics and spectroscopy and motivate future applications to larger uranium-containing systems.

Our purpose is to revisit the screw theory in light of the affine tensor formalism, introducing the co-momentum and momentum tensors. Our target-applications of the Euler-Poincaré equation are problems of mechanics such as the motion of the rigid body or the statics and the dynamics of Cosserat arches, in relation to the concept of momentum tensor. Using the framework of Ehresmann connections on the principal bundle of affine frames, we show that the Euler-Poincaré equation means that the momentum tensor is parallel-transported.

We consider the Boolean model of continuum percolation, where points are placed in $\mathbb{R}^d$ by a Poisson point process and pairs of points with distance at most 1 are connected by an edge. The time constant is the limiting ratio of the chemical distance (i.e. graph distance) to the Euclidean distance for pairs of distant connected points. Yao, Chen, and Guo established the existence of a time constant in the supercritical regime. We show that above the critical intensity, the time constant is a Lipschitz continuous function of the intensity. The proof adapts a recent argument of Can, Nakajima, and Nguyen to the continuous setting.

Routinely collected data, such as electronic health record (EHR) data, are frequently used for biomedical research, but these data are prone to errors, which can bias study findings. Validating data in subsamples of records can reduce bias, and the efficiency of estimates can be improved by incorporating in analyses both the error-prone data available on the entire cohort and the validated data available on the subsample. One approach to incorporate both data sources is with generalized raking, which calibrates validation sampling weights using error-prone data from the entire cohort. Motivated by an EHR study of maternal weight gain during pregnancy with a validation subsample, we develop and illustrate generalized raking techniques for cumulative probability models (CPMs). CPMs are robust, rank-based and semiparametric models for continuous, ordinal, or mixed type outcome data. We develop efficient generalized raking estimators for CPMs, evaluate their performance relative to competing methods, and demonstrate the utility and strengths of generalized raking with CPMs in a study that examines factors associated with weight gain during pregnancy.

Gamma-ray bursts temporal profile can be extremely variable, going from a single pulse of a few seconds duration to multiple superimposed pulses occurring over tens or even hundreds of seconds. The variability displayed in the lightcurve of each gamma-ray burst can be the result of the activity taking place in the central engine that generates these violent phenomena, as well as due to magnetic reconnection activities at larger distances. The objective of this work is to find the shortest variability hidden in the lightcurves of the GRBs, with particular focus for the ones with measured redshift, on timescales as short as few milliseconds. This variability will then be related to physical characteristics of the central engine, and evidences of its relation with the spectral parameters of the burst, such as the isotropic energy and peak energy, will be presented. This research is even more relevant in view of the future generation of satellites with improved timing resolution, that will allow us to explore the possible variability in the microsecond region.

We introduce a stochastic interacting particle system in separable Hilbert spaces together with its associated mean-field formulation. The model is shown to retain the characteristic consensus-driven structure of classical Consensus-Based Optimization, while accounting for the analytical challenges of infinite-dimensional dynamics. We establish well-posedness of the proposed dynamics and analyze the associated consensus mechanism. Furthermore, we derive convergence guarantees under suitable assumptions on the objective functional, showing concentration of the dynamics toward the minimizer in the long-time regime. This extends the applicability of the method to a broad class of infinite-dimensional optimization problems. In addition, we study the corresponding finite-particle system relevant for numerical implementation and propose a practical algorithm.

Repurposing natural gas pipelines for hydrogen transport requires understanding how external defects, like dents and gouges, affect structural integrity under H$_2$ exposure. To address this, we combine experiments with a new hydrogen embrittlement model aimed at large plastic straining scenarios, which integrates: (i) multi-trap hydrogen transport, (ii) finite-strain plasticity, and (iii) a hydrogen- and triaxiality-dependent damage law. Each constituent of the model is validated with experiments on X65 pipeline steel: (i) hydrogen permeation, (ii) full-scale pipe-indentation, and (iii) mechanical testing at different hydrogen and triaxiality levels. The validated model is used to study \textit{passive} (indent before H$_2$ exposure) and \textit{active} (indent with H$_2$) dents and gouges. Results reveal that hydrogen does not significantly increase the damage severity of those defects, unless hydrogen egress is completely precluded at the outer surface of a pipeline that is being pressurised internally and contains a pre-existing \textit{passive} dent with a gouge.