AI for Science

The Global Alliance for Genomics and Health (GA4GH) Beacon protocol lets researchers ask whether a genomic variant has been observed in a participating cohort and receive aggregate variant-level counts. As Beacon networks grow, two privacy risks remain: host institutions can see plaintext queries, and repeated rare-variant queries can support membership-inference attacks. We present bioETH-Beacon, a smart-contract prototype that runs the Beacon "aggregate count" query over encrypted data on a fully homomorphic Ethereum Virtual Machine (fhEVM). Hospitals upload encrypted marker-count entries, authorized researchers submit encrypted marker queries, and the contract returns an encrypted answer that is released, via an off-chain key-management service, only to the requester named in the contract's on-chain ACL. The design is organized as a 3x4 tier-by-query-family grid spanning genotype, sex, age, and phenotype queries, with tiers that trade stronger confidentiality for lower query cost. For genotype paths, the prototype can add bounded on-chain noise to mitigate probing attacks. Experiments on synthetic panels derived from a Polygenic Score (PGS) catalog show the expected scaling behavior and demonstrate that pre-aggregation can substantially reduce query gas when public marker presence is an acceptable trade-off. Overall, bioETH-Beacon provides a research prototype for confidential Beacon-style genomic querying without a trusted compute evaluator.

We present the first systematic and comprehensive scan of two-flavon Froggatt-Nielsen (FN) models, employing artificial intelligence techniques to explore the high-dimensional, mixed discrete-continuous parameter space. Extending the standard single-flavon FN framework to a two-flavon setup in which separate flavon fields couple independently to the up- and down-type sectors, we demonstrate that the relative phase between their vacuum expectation values (vevs) provides a natural and generic source of CP violation absent in single-flavon models. To explore this enlarged model space, we cast the search for phenomenologically viable models as a multi-objective optimisation problem, formulating each experimental constraint as a separate objective, and employ the Non-dominated Sorting Genetic Algorithm III to simultaneously fit all 18 FN charges, 45 Wilson coefficients, and flavon parameters to both the quark and lepton sectors. Our approach requires no separate training phase and identifies phenomenologically viable models orders of magnitude faster than prior reinforcement learning methods. Imposing experimental constraints on CKM and PMNS mixing angles and CP phases, charged fermion masses, and neutrino squared-mass differences, we discover over $100\,000$ unique viable models with a remarkably low duplication rate, indicating that the space of valid two-flavon FN realisations has not been exhausted. Both Normal and Inverted neutrino mass squared orderings are realised, with the relative hierarchy between the flavon vevs producing qualitatively distinct predictions for the effective neutrinoless double beta decay mass $m_{ee}$. We further demonstrate the existence of minimal FN realisations with maximal flavon exponent as small as three, and of models reproducing charged fermion masses to within $6\%$ without any dedicated continuous parameter optimisation.

Large-scale hypothesis testing supports probability claims about individual hypotheses, as in empirical Bayes methods for estimating local false discovery rates. We study how such claims can be interpreted as approximately calibrated forecasts of the null hypothesis, yielding interpretable error probabilities even under model misspecification. Our approach draws conceptual inspiration from probabilistic forecasting but addresses a different challenge: unlike forecasting, where labels are eventually observed, in multiple testing the ground truth is never revealed, so calibration must be assessed stochastically and established indirectly. We address this challenge by constructing a set of pseudo-labels, derived from the spacings of ordered $p$-values, which have the local false discovery rate as their regression target. Our construction unlocks existing tools for assessing and performing post-hoc calibration in multiple testing. Notably, we find on a large-scale empirical survey of published psychology and neuroscience literature that the $q$-value, a popular error measure based on the false discovery rate, can be severely miscalibrated.

Gene regulatory networks (GRNs) are fundamental to cellular growth and tissue formation, orchestrating spatially and temporally regulated gene expression during development. These networks are inherently subject to intrinsic fluctuations arising from molecular noise, making the analysis of their stability essential for understanding robust pattern formation and developmental dynamics of the organism. In this study, we analyze the stability and dynamics of cyclic GRNs with negative feedback and diffusion, considering both deterministic and stochastic approaches. In the deterministic case, the system exhibits a bifurcation between stability and instability, leading to Hopf instability in the absence of diffusion and to Turing-Hopf instability when diffusion is included. It was observed that the discretization of the spatial domain introduces additional unstable modes, enabling a wider range of patterns. The stochastic framework based on the second-moment approach, which incorporates intrinsic fluctuations, reveals that for small system sizes, fluctuations can dominate the dynamics and induce stochastic Turing instability, even when the system is stable in the absence of diffusion. Notably, Turing instabilities can emerge even when all variables have the same diffusion rate. The developed framework provides a systematic method for analyzing the stability of high-dimensional stochastic systems with diffusion, thereby simplifying the prediction of Turing and Turing-Hopf instabilities. These findings contribute to a deeper understanding of the complex dynamics and pattern formation in GRNs, with potential implications for biological processes, such as cellular differentiation and development.

Motivation: Biomedical question answering often requires evidence beyond topically retrieved literature, including gene alias resolution, database identifier normalization, and atlas-derived biological measurements. However, existing retrieval-augmented generation (RAG) systems typically follow a fixed workflow and lack an explicit mechanism for deciding when retrieved text is sufficient, when curated biomedical knowledge is required, or when executable evidence assembly over structured measurements should be invoked. This motivates a substrate-aware large language model (LLM) harness that selectively assembles sufficient evidence across literature, knowledge bases, and biological atlases. Results: We introduce BioHarness, an LLM harness for staged biomedical evidence assembly across literature retrieval, curated biomedical knowledge resources, and atlas-derived structured measurements. BioHarness first attempts to answer from reranked literature evidence and escalates through grounded cascade control to REPL-style evidence assembly only when the current evidence is uncertain, weakly grounded, or substrate-mismatched. Across 19,302 biomedical QA items spanning seven answer formats, BioHarness improves the pooled score from 65.9 to 71.0 over the strongest non-oracle baseline. Ablations, case studies, and backbone-scaling analyses show that these gains arise from repairing evidence-substrate mismatches through reranking, entity grounding, and structured measurement access, rather than from indiscriminately invoking more reasoning steps, retrieving additional literature, or relying on a particular answer-model scale.

Competing risks are commonly observed in engineering fields and can bring challenges to time-to-event data modeling when the application scenarios are complicated. Recently, deep neural networks have received great attention for prediction with competing risks, due to their flexibility and high learning capability. However, the complexity of neural network structure brings extra difficulty in hyperparameter tuning based on different data inputs. Additionally, when an engineered system has complex physical structures with multiple hierarchical levels, treating all structural levels as a single group of inputs may fail to capture critical information. To address the issues, we propose a Structured Segmented Hazard Deep Neural Network (SSH-Net) for failure time prediction under cause-specific competing risks framework. Our approach associates neural network structure with data structures, and allows different covariate groups to impact the failure prediction through separate sub-networks. The neural network is constructed based on a cause-specific competing risks model. The SSH-Net outputs cause-specific hazard functions, and utilizes the penalized log-likelihood as the loss function. The prediction accuracy of SSH-Net is validated through simulation studies by evaluating the Brier score, the area under receiver operating characteristic curves (AUC), and the root mean square error (RMSE) of the predicted cause-specific cumulative incident function. We further demonstrate the model's ability to predict failure time distribution functions using the Titan GPU failure time data.

Motivated by the privacy, sensitivity and sharing limitations of health data, we present a comprehensive pipeline for inference of Bayesian mixture models within a federated learning setting, i.e. when data cannot be fully shared or pooled across compute nodes. We adopt a Consensus Monte Carlo (CMC) approach, in which an MCMC algorithm is run independently within each data silo to estimate local posterior distributions, which are then aggregated to approximate the posterior over the full data. The variational CMC approach of Rabinovich, Angelino and Jordan (2015) [1] frames the aggregation step as a variational inference problem, but their application to mixtures assumes the number of clusters and key mixture parameters to be known. Our main methodological contributions are: (i) an extension of variational CMC to over-fitted Bayesian mixture models that infer the number of clusters and all model parameters, without requiring conjugacy; (ii) novel cluster-matching algorithms suitable for cross-silo settings in which not every cluster appears in each local dataset; (iii) a number of inference strategies for the aggregation step, matched to different federated learning constraints; and (iv) guidelines for choosing among these in practice. A comprehensive simulation study validates the framework and allows us to compare to state-of-the-art federated learning alternatives. Notably, we show that when the composition of local datasets reflects the underlying clustering structure in the data, our approach can recover small clusters with greater accuracy than standard MCMC applied to the pooled data. We illustrate the framework on large-scale electronic health record data, identifying multi-morbidity patterns in a British geriatric population.

We consider contraction of Bayesian posterior distributions in nonparametric settings where coefficients of a function over a basis or dictionary are given priors with $p$--exponential tails, including Laplace tails $(p=1)$ and heavier tails $(p<1)$. It is shown that contraction rates improve as $p$ decreases and that full adaptation to smoothness, up to logarithmic factors, is obtained in an appropriate $p\to 0$ regime. As applications, we consider both series priors in white noise regression and shallow ReLU neural networks in random design regression. In particular, we show that overparametrised shallow ReLU networks can adapt to any regularity $0\le β\le 2$. Through a simulation study, we show strong empirical agreement with the behavior predicted by our theory.

We introduce Vistas, a tool for visualizing high-energy particle physics collisions simulated by the Pythia Monte-Carlo event generator. Vistas utilizes the browser-based event display framework Phoenix to show distinct computational stages of a high-energy collision event simulation: the hard process, parton shower, hadronization, and particle decays. Particles produced from each of these stages are represented as lines in an interactive three-dimensional graph structure, where each line is along the direction of its particle's three-momentum vector. The event can be rotated, translated and zoomed, and details for each particle can be accessed by selecting the relevant particle line. Additionally, particle lines from all stages of the simulation can be toggled on and off and can be filtered by particle-level kinematic selection requirements. This interactive environment provides an intuitive interpretation of Pythia simulation output, including detailed features such as color flow, beam remnants, and multiple parton interactions, making it a useful tool in physics education settings, from outreach activities to graduate particle-physics courses.

Charged-particle tracking -- reconstructing trajectories from sparse detector measurements -- is a fundamental high-energy-physics inference problem and a canonical example of learning under extreme combinatorial ambiguity. At the High-Luminosity Large Hadron Collider (HL-LHC), tracking must remain accurate and efficient despite unprecedented collision densities. Graph neural networks perform strongly, but incur substantial costs from graph construction and processing, while transformer-based approaches rely on auxiliary stages that prevent end-to-end optimization. To address this, we present HEPTv2, an end-to-end point-transformer architecture that reconstructs tracks from detector hits in one trainable pipeline. HEPTv2 combines a locality-aware point encoder with a track decoder that predicts complete trajectories without graph-building, clustering, or filtering. The encoder uses locality-sensitive hashing in detector coordinate space to preserve tracking-relevant geometry while enabling efficient local attention. The decoder resolves ambiguities through sectorized decoding and direct hit-to-track prediction under joint encoder-decoder supervision, allowing the full pipeline to be optimized end-to-end. On TrackML, HEPTv2 achieves 98.6% double-majority tracking efficiency at a 0.8% fake rate, while requiring only $\sim$15~ms inference time and 0.4~GB peak memory per event on a NVIDIA A100 GPU. Latency and memory scale approximately linearly for events with up to $5\times10^5$ hits. HEPTv2 establishes a new state of the art in the accuracy-latency trade-off, improving efficiency by 4.5% over the strongest prior transformer and by 1.1--2.2% over optimized graph-based pipelines, while reducing latency by factors of 7 and 38--52, respectively. These results show end-to-end transformers can deliver the accuracy and efficiency required for real-time particle reconstruction at the HL-LHC.

We introduce a novel active-learning framework for failure probability estimation in structural reliability analysis that integrates Active Kriging Monte Carlo simulation with conformal prediction. The proposed approach employs an adaptive cross-conformal strategy specifically designed for small-sample settings and kriging surrogate models using the J+GP conformal estimator. Unlike standard AK-MCS methods, the proposed framework provides distribution-free guarantees on prediction errors, leading to more reliable classification of samples near the limit-state surface. This improved uncertainty quantification enhances both the accuracy and robustness of failure probability estimates, especially for rare-event regimes where such efficiency is crucial. Reproducible numerical results illustrate the effectiveness of the method and also compare it to classical approaches on well-established benchmarks.

Factor models are popular approaches for analyzing high-dimensional data to extract low-rank signals and estimate covariances. They decompose the covariance matrix as the sum of low-rank and diagonal components. A key issue is how to choose the latent dimension $k$, which is particularly challenging when the factor model only holds approximately and in low signal-to-noise scenarios. Bayesian overfitted factor models specify an upper bound on $k$ and rely on structured shrinkage priors to effectively remove extra components. Such approaches are popular and effective, but computationally expensive. We propose a much faster \texttt{EigenBayes} approach that provides valid uncertainty quantification, based on spectral estimation of latent factors and adaptive empirical Bayes calibration of key hyperparameters. The resulting posterior distribution factorizes across outcomes and is analytically tractable, bypassing Markov chain Monte Carlo. We show that \texttt{EigenBayes} adapts to the signal-to-noise ratio of each outcome and latent dimension, while shrinking superfluous latent components to zero. We establish favorable asymptotic properties and demonstrate strong empirical performance in numerical experiments and a genomics application, where EigenBayes outperforms state-of-the-art alternatives.

Brain network is commonly divided into modules for analyzing their functionally segregated roles for group-level analysis in neuroimaging studies. Here, we introduce stochastic modules within brain networks for a robust probabilistic measurement of structural-functional module consistency (SFMC) in a group of subjects. Specifically, a stochastic module can be regarded as the chance of a brain region across subjects potentially being assigned to a group-level sub-network, characterized as an assignment probability for this brain region. This novel method has two advantages for evaluating inhomogeneous modules in brain networks. The first is that it can robustly evaluate the consistency between brain structural and functional modules whose population sizes are not necessary the same, and the second is that it is able to take into account the inter-individual variability of the modules for the groups. Moreover, compared with the conventional structural-functional coupling approach, our stochastic module-based method reveals a more pronounced decline in the coupling between structure and function, indicating stronger developmental reorganization. Our results using the dataset from Baby Connectome Project (BCP) show that the SFMC decreases from 0 to 5 years old, and is greater in primary brain regions, such as visual areas, while lower in more advanced cognitive regions, including those related to attention, control, and default mode network.

Seasonal influenza infects millions of people and causes substantial morbidity and mortality in the United States each year, making accurate short-term forecasting a core public-health need. Reliable forecasts of epidemic time series can inform vaccination timing, hospital staffing, and resource allocation, yet the comparative behavior of modern forecasting architectures on infectious-disease surveillance data remains insufficiently characterized. We address this gap through a systematic evaluation of regional influenza forecasting using influenza-like illness surveillance and influenza-associated hospitalization time series under both temporal and spatial generalization settings for 1-4-week-ahead prediction. We compare classical neural network architectures, numerical transformer-based models, pretrained time series foundation models, and LLM-based forecasting approaches. Across tasks, we demonstrate that a mixture-of-experts model that fuses multiple pretrained forecasters achieves the strongest overall performance, indicating that heterogeneous pretrained representations provide complementary predictive information. Our results further show that numerical transformer-based models produce reliable forecasts, while pretraining provides the largest gains at longer horizons, particularly when the pretraining domain is mechanistically aligned with influenza dynamics. In contrast, LLM-based time series methods underperform relative to numerical forecasters in this setting. Finally, we examine hospitalization information as both an auxiliary covariate and a pretraining source. Hospitalization signals provide complementary improvements in selected settings and clarify when additional surveillance streams enhance the robustness of multi-horizon forecasting. These findings provide actionable guidance on model selection, pretraining strategy, and auxiliary-signal use for influenza preparedness.

We present a machine-checked completeness theorem, in Lean 4, for the hybrid logic $L(\forall)$: propositional modal logic with nominals, the satisfaction-style binder $\forall$, and the box modality. (Machine-checked completeness for basic hybrid logic, without binders, was pioneered by Asta Halkjær From in Isabelle/HOL.) We build on Alex Oltean's 2023 Lean 4 formalization, which mechanized the syntax, semantics, Hilbert-style proof system, and soundness following Blackburn's Hybrid Completeness (1998), but left completeness unfinished. Finishing it requires manufacturing fresh names at two structurally different points, and our central finding is that they call for two different tools. (1) The root witnessed maximal consistent set, built by an extended Lindenbaum construction, needs at each step a nominal fresh for the whole set; the right tool is structural freshness: extend the language so an infinite supply of nominals is reserved by construction. We survey the design space (Oltean's odd/even encoding inside $\mathbb{N}$, the disjoint-sum $N \oplus \mathbb{N}$ parameterization suggested by Bud Mishra, and From's synthetic-completeness frameworks) and explain the encoding we adopt. (2) The witnessed $\Diamond$-successor of a maximal consistent set cannot be obtained this way: its canonical box-reduct provably mentions every nominal, so no reserved name is fresh. Here the right tool is one Oltean chose but left incomplete: an existence-lemma Henkin construction drawing each witness from the predecessor's witnessedness through a fresh state variable; we complete it with a data-carrying witness accumulator and a compactness argument. The theorem $Γ\models φ\to Γ\vdash φ$ is fully formalized: the development is sorry-free, and #print axioms reports only propext, Classical.choice, and Quot.sound. We port the development to Lean v4.30.0 / mathlib v4.30.0.

Inferring epidemiological parameters from transmission trees is essential for understanding infectious disease dynamics. Existing tree-based likelihood methods, including the multi-type birth-death models originally applied in phylodynamic settings, provide powerful tools, but most assume homogeneous mixing and rarely capture how transmission potential changes as an individual infects more of their contacts. In this work, we develop a likelihood framework that operates directly on transmission trees, in which nodes are individuals and edges are reported transmission events, with no sequence data involved. We derive a likelihood for a stochastic SIR process on a rooted contact tree in which each infected individual is characterised by the total number of effective contacts, and the number of already infected downstream contacts. We obtain closed-form ordinary differential equations for the probability that a clade goes entirely unobserved and for the probability density that it produces an observed (sampled) tip in a given state. The resulting likelihood can be evaluated for a rooted contact tree with known tip states, and we extend it to partially resolved trees by treating internal branching times as latent variables. Validation on simulated outbreaks confirms accurate parameter recovery and well calibrated uncertainty. Application to empirical COVID-19 contact-tracing data from Karnataka, India, demonstrates the framework's utility for real epidemiological settings. By incorporating contact-degree heterogeneity in a multi-type branching likelihood, our work provides a principled baseline for inferring both transmission dynamics and contact structure from fully or partially resolved transmission trees, complementing rather than relying on sequence-based phylodynamic inference

Bilevel optimization is an indispensable modeling tool for modern machine learning and engineering design. However, the theory and practice for finding second order stationary points in the context of bilevel optimization still remain largely unsettled. Even for bilevel optimization with strongly convex lower-level problem, the hyperfunction it induces is in general nonconvex. Although the Cubic Regularized Newton methods (CRN) famously achieve the optimal $\mathcal{O}(\varepsilon^{-1.5})$ SOSP (second-order stationary point) rate in single-level optimization, it is unclear how to control the accuracy of the hypergradient and hyper-Hessian computations in the context of applying the second-order methods to bilevel problems in order for the overall process to be efficient. In this paper, we set out to answer this question. In particular, we first formulate a double loop CRN baseline that achieves the optimal outer rate but requires repeated lower level solves. Next, we propose a single loop cubic regularized Newton algorithm that combines one lower-level gradient step with one Newton step for the hypergradient, and prove an overall deterministic $\mathcal{O}(\varepsilon^{-1.5})$ total oracle complexity, which is optimal. In addition, we illustrate that some intuitively simple modifications of our method may fail to hold up the convergence result. To the best of our knowledge, this is the first deterministic single loop method for unconstrained NCSC (non-convex upper-level and strongly convex lower-level) bilevel optimization setting that achieves the $\mathcal{O}(\varepsilon^{-1.5})$ optimal convergence rate for finding an $\varepsilon$-SOSP of the hyperfunction.

Soil microorganisms control organic matter cycling and largely determine how soil systems can cope with and mitigate climate change and environmental threats. Representing microbial dynamics in process-based soil models is therefore critical to predict carbon cycling in soils, albeit highly challenging to inform from data. One promising approach to improve their parametrisation is the integration of genomic data, yet modelling the complex and unknown relationship between genomes and the processes the microbes are driving is an unsolved problem. In this work, we present the first hybrid modeling framework for deriving biokinetic parameter values of a process-based soil organic matter turnover model from metagenome-inferred functional traits based on DNA sequencing data. Our model predicts biokinetic parameters of the process-based model from genomic trait data with a neural network and integrates constraints from ecological theory and literature to ensure realistic behavior, even of non-observed state variables. We evaluate our method on synthetic genomic trait datasets of varying complexity and on real data, showing that our approach improves performance over multiple baselines and learns the dynamics of unmeasurable components of the process-based model effectively, even for small training datasets.

We forecast future volatilities and correlations of financial markets based on the current trends in these markets. This complements previous work that models future expected returns by a cubic polynomial of the current trend strength. Empirically, we observe that volatilities and correlations tend to increase day after day in times of strong up- or down-trends. This effect is particularly pronounced in down-trends. It can be accurately quantified by quadratic polynomials of today's trend strengths, which refine common mean-reversion models of volatilities and correlations. Our results improve the prediction of market risk by accounting for market trends. They also support a recent proposal to model financial markets by a lattice gas near its critical point.

This work follows the evolution of financial networks in Norway over a period of nine years at a monthly rate. The data consist of board directors and their affiliations to companies, which we model as simplicial complexes. In this framework, directors are represented as nodes and companies as faces of the complex. To characterize the latter, we focus on three topological measures: the Euler characteristic, computed through the Betti numbers, torsion computed through the reduced determinant of the higher-order Laplacians, and higher-order clustering coefficients. The first two fail to capture the effect of imposed law on representation, unlike our notion of curvature which is a geometrical measure computed from the coefficients of the series expansion of the heat kernel in powers of time, which is our major contribution in this work. In particular, the Euler characteristic integrates curvature, and thus local information is lost. Subsequently, not every topological measure can reliably capture shocks in networks. Further, the number of spanning trees may undergo significant changes at the lowest order, yet these changes need not be reflected in the torsion. Conversely, the change in the curvature revealed variation in the board interlock due to legislation, and serves as a sensitive measure for detecting shocks in networks. Inflection points in curvature are associated with external forcing, and minima with shock arrival times. Sharp transitions are also observed in the components of torsion, while smooth changes are observed in higher-order clustering.

Gene regulatory networks govern cellular fate decisions through multistable dynamics. The genetic toggle switch is a canonical model of such behaviour; yet, the impact of cell division on its dynamics remains poorly understood. We derive analytical separatrices for a simplified Boolean toggle switch with and without division. We show that division can redirect trajectories with identical initial conditions to opposing stable states, and we define a region of disagreement where fate decisions are predicted incorrectly if division is neglected. Our results imply that division can fundamentally reshape fate boundaries in multistable regulatory networks.

We extend the theory of root clusters from perfect fields to general fields which are not necessarily perfect. We introduce the following notions for field extensions over any given base field and study their interesting properties: root cluster size, multicluster size and their generalizations root capacity, multiroot capacity; ascending index, ascending normal index and their generalizations intersection indicium, intersection normal indicium; compositum indicium and compositum normal indicium. We establish our results on the Inverse problems for these generalized notions over Hilbertian fields which generalizes our earlier results which were over number fields. In particular, we show over a given Hilbertian field, the existence of a polynomial for given degree, cluster size and multicluster size and existence of an extension for given root capacity and multiroot capacity with respect to that polynomial.

We show that for any $A\subseteq \mathbb{F}_q^n$ lacking non-trivial solutions to a translation-invariant linear equation of genus one, meaning that no nonempty proper subset of the coefficients sums to $0$, there is a set $B\subseteq \mathbb{F}_q^m$ in some higher dimension which also lacks non-trivial solutions, such that \[|B|^{1/m}>|A|^{1/n}.\] In particular, this implies that no fixed cap set in $\mathbb{F}_3^n$ gives an asymptotically optimal lower bound by direct products alone.

Learning Bayesian network (BN) structure from sparse discrete data is hard: when each instance records only a few variables, most variable pairs lack the joint observations needed for reliable scoring, and data-only methods recover little structure. However, imperfect domain knowledge, expressible as a weighted directed knowledge graph (KG), is often available. We propose KG-SoftMAP, which encodes such a KG as a finite-strength, confidence-weighted edge prior and maximizes a MAP objective combining the BDeu score with a logit-form prior; the KG may be expert-curated or LLM-extracted. On synthetic benchmarks with known DAGs, KG-SoftMAP reaches Directed-F1 (DF1) $0.19$--$0.32$ at observation rate $ρ=0.05$ and DF1 $0.44$--$0.97$ at $ρ\geq0.2$, while every data-only learner tested stays near zero under the same sparse masks. Recovery tracks KG quality: controlled corruption degrades it smoothly, a zero-signal KG yields DF1 $0.00$, and a blindly LLM-extracted KG with imperfect precision and recall still drives substantial recovery. On three real sparse educational datasets, the learned BN acts as a concept-level posterior model: on SAF it matches logistic regression (LR) within $0.03$ F1_FAIL while providing an inspectable concept graph, calibrated Fail probabilities, and tractable posterior queries from partial observations.

Recently, Starr used asymptotic methods to disprove a conjecture by Heim--Neuhauser and Abdesselam about the log-concavity of the D'Arcais polynomials, without giving an explicit counterexample. We refine the asymptotics, to give the necessary estimates on convolutions of $σ_{-1}$, and identify the first counterexample at $λ= 65\,214\,507\,758\,400$. We also consider the asymptotic density of such counterexamples.

A finite group is said to be quartic-free if its order is not divisible by $p^4$ of any prime $p$. A finite group is called an $A$-group if all of its Sylow subgroups are abelian. Objective of this paper is to provide explicit structure of a quartic-free $A$-group. Further in the process of providing the explicit structure we also determine the derived length of a solvable quartic-free $A$-group.

The geometry of an object plays a vital role in modulating its interactions with the physical world. It nevertheless remains difficult to describe geometric information numerically for the purposes of statistical inference or classification tasks. Here, we introduce a new topological transform which leverages directional piecewise-linear Morse theory to quantify the geometry of an embedded object by cataloguing critical points across multiple height-functions. The output of this Morse transform records both the heights and the local topological type (peak, trough or saddle) of the critical points that characterise the underlying shape, retaining finer information than the Euler characteristic transform whilst naturally prioritising a shape's outermost regions. Crucially, this output can be further compressed into a rich but compact feature vector. We benchmark the Morse feature vector as a descriptor for ligand-based virtual screening (LBVS), which intrinsically depends on the shape of molecules. Under a common gradient-boosted tree classification pipeline, Morse descriptors achieve the highest mean AUROC when compared to other topological transform descriptors and to standard shape-based LBVS descriptors.

Data encountered in practice are frequently contaminated by additive noise, and wavelet shrinkage remains a fundamental tool for recovering underlying signals in nonparametric estimation. Classical procedures such as hard and soft thresholding decide whether to retain a wavelet coefficient almost entirely from its magnitude. Although effective in many settings, these rules can be too rigid for coefficients whose magnitudes fall in an intermediate region where the distinction between signal and noise is uncertain. We propose MLShrink, a two-threshold wavelet denoising procedure that combines wavelet shrinkage with machine learning. Coefficients below a lower threshold are discarded, coefficients above an upper threshold are retained, and coefficients in the intermediate band are classified using local wavelet-domain features. In this way, MLShrink preserves the simplicity of classical thresholding away from the decision boundary while allowing data-adaptive decisions for ambiguous coefficients. The paper also develops a theoretical framework tailored to this architecture. We show that MLShrink is a nonexpansive support-selection rule, derive an oracle-based risk decomposition showing that excess denoising risk is determined by classification errors on the undecided band, and establish an oracle-consistency result under suitable assumptions on classifier performance. Simulation experiments on standard benchmark signals indicate that MLShrink is competitive with several established wavelet shrinkage methods and is especially effective for signals with irregular, edge-rich, or non-smooth structure. These findings suggest that learned decisions on the intermediate threshold band provide a useful and interpretable connection between classical wavelet denoising and modern statistical learning.

Haematocrit influences blood viscosity and may affect coronary computational fluid dynamics (CFD). However, previous studies examined broad or pathological haematocrit ranges, and it remains unclear whether female-specific haematocrit variations within the physiological range produce meaningful changes in coronary haemodynamics. 15 female coronaries were analysed, including healthy arteries and diseased models with mild, moderate and severe stenosis. A haematocrit-dependent Carreau-Yasuda model was developed. CFD simulations were performed using the standard rheology model and a female-specific haematocrit-based model (40%). Time-averaged endothelial shear stress (TAESS), ESS gradient (ESSG), temporal shear variation index (TSVI), helicity, and low/high TAESS exposure were compared across coronary trees, arterial segments, bifurcations, stenosed vessels and corresponding narrowed regions. The female-specific model produced statistically significant differences from the standard model across all metrics and coronary regions (p < 0.05). However, the absolute differences were small, indicating a limited haemodynamic impact. Bland-Altman analysis showed narrow biases and limits of agreement. Linear regression demonstrated significant associations between inter-model differences and haemodynamic magnitude for TAESS, ESSG, helicity intensity, and adverse TAESS exposure, but the slopes were small. Similar findings were observed in stenosed arteries, where both models captured comparable flow disturbances across stenosis severities. Female-specific haematocrit variation within the physiological range is computationally detectable but haemodynamically negligible in coronary CFD. A standard rheology model is therefore likely sufficient for most coronary CFD studies, while personalised haematocrit modelling is more relevant for patients with abnormal haematocrit or rheology-focused studies.

The geochemical evolution of long-lived magma oceans is strongly regulated by volatile exchange between the molten mantle and the atmosphere. For planets inside the runaway-greenhouse limit, this coupled evolution can persist for billions of years. However, most existing studies assume Earth-like (oxidized) conditions and neglect the influence of redox state on melt thermodynamics and volatile release. We quantified how experimentally derived, oxygen-fugacity-dependent melting curves implemented within the coupled interior-atmosphere framework PROTEUS propagate into the thermal structure, melt fraction, and rheological evolution of rocky exoplanet interiors, applying this to the short-period super-Earth GJ 1132 b. We found strongly non-linear thermal responses to variations in melting curves. In volatile-poor systems, reduced melting curves promote earlier deep-mantle crystallisation relative to oxidised and Earth-like cases, favouring late-stage surface magma oceans sustained by greenhouse warming, while oxidized melting curves maintain higher melt fractions and a vertically extended magma ocean. Reduced mantles produce massive H$_2$-CO-rich atmospheres; oxidized mantles favour thinner H$_2$O-CO$_2$ envelopes. In volatile-rich systems, the interior reaches radiative equilibrium at high melt fractions, sustaining a steady-state global magma ocean in which melting curve variations do not significantly influence solidification timing. This indicates a hierarchical control: volatile inventory and surface oxygen fugacity act as the primary regulators of thermal state, while oxygen-fugacity-dependent melting relations provide a secondary modulation. These contrasting regimes produce distinct atmospheric compositions and formation timescales, offering testable spectral predictions for close-in rocky exoplanets evaluable with forthcoming JWST observations.