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arXiv2026

Beyond AHI: An Interpretable Causal-Discovery-Guided Framework for Sleep Recovery in Connected Health

Objective sleep assessment relies on polysomnography (PSG), yet clinical impact is often better reflected in patient-reported outcomes (PROs) such as sleepiness and fatigue. Existing summary indices, including the Apnea-Hypopnea Index (AHI), provide limited insight into the multidomain physiology underlying functional recovery. We propose an interpretable, causal-discovery-guided framework for deriving a hierarchical Sleep Recovery Score (SRS) from multimodal PSG. Using two large population cohorts (MESA: $n=1{,}540$; MrOS: $n=825$), we apply directed acyclic graph (DAG) learning to identify candidate physiological drivers spanning respiratory burden, hypoxic burden, sleep fragmentation, sleep architecture, and autonomic regulation. Although derived from clinical PSG, these domains map naturally to sensing streams increasingly available in connected health technologies, including wearable ECG, oximetry, and sleep-stage estimation devices. To preserve mechanistic plausibility, we introduce a two-stage screening process that combines physiology-based constraints with constrained LLM-assisted auditing to identify and remove structural confounders and construct-overlapping variables. Across cohorts, these five domains emerge as recurrent physiological domains associated with recovery, and the resulting SRS shows up to $3.4\times$ stronger alignment with perceived recovery than AHI. By linking multimodal sleep physiology to patient-centered outcomes through an interpretable, bias-aware, and domain-structured framework, this work provides a practical foundation for recovery modeling across both clinical sleep studies and emerging smart and connected health settings.

cs.LG↗

arXiv2026

Combating Organized Platform Abuse: Amplifying Weak Risk Signals with Structural Information

Large-scale online service platforms face severe challenges from organized platform abuse: multiple forms such as credit card fraud and promotion abuse continually emerge, characterized by large numbers of involved accounts, rapid outbreaks, and constantly shifting tactics. Existing mainstream approaches, whether heuristic rules limited in precision, supervised learning with insufficient generalization, or graph models that are engineering-heavy and dependent on seed users, have failed to address such threats effectively. This paper returns to first principles and, starting from the economic constraints of fraudulent behavior, proposes the Fraudster's Trilemma: organized attackers cannot simultaneously achieve scale, low cost, and dispersed cash-out. Building on this theory, we derive a robust structural invariant in organized fraud, namely centralized cash-out, and use a simple statistical method to turn low-precision individual weak signals into high-precision strong decisions. The method requires no labels, is nearly parameter-free, white-box interpretable, has linear complexity O(|E|), avoids cold-start issues, and its detection logic possesses the "open-hand" property: attackers cannot evade it even when fully informed. We validate the approach on two real fraud incidents in backtests. In the promotion abuse case, a single near-zero-cost weak signal (global Precision of only 16%) after structural amplification achieves Precision above 91% and Recall exceeding 99% (z=10.0); at a higher threshold (z=40.0), Precision reaches 93.7%. In the credit card fraud case, an infrastructure-layer weak signal (device spoofing) successfully detects payment-layer attacks without any business-logic linkage, revealing the framework's natural MO-agnostic property: it relies more on the structural invariant than on signal semantics.

cs.CR↗

arXiv2026

Biases in Expected Goals Models Confound Finishing Ability

Expected Goals (xG) has emerged as a popular tool for evaluating finishing skill in soccer analytics. It involves comparing a player's cumulative xG with their actual goal output, where consistent overperformance indicates strong finishing ability. However, the assessment of finishing skill in soccer using xG remains contentious due to players' difficulty in consistently outperforming their cumulative xG. In this paper, we aim to address the limitations and nuances surrounding the evaluation of finishing skill using xG statistics. Specifically, we explore three hypotheses: (1) the deviation between actual and expected goals is an inadequate metric due to the high variance of shot outcomes and limited sample sizes, (2) the inclusion of all shots in cumulative xG calculation may be inappropriate, and (3) xG models contain biases arising from interdependencies in the data that affect skill measurement. We found that sustained overperformance of cumulative xG requires both high shot volumes and exceptional finishing, including all shot types can obscure the finishing ability of proficient strikers, and that there is a persistent bias that makes the actual and expected goals closer for excellent finishers than it really is. Overall, our analysis indicates that we need more nuanced quantitative approaches for investigating a player's finishing ability, which we achieved using a technique from AI fairness to learn an xG model that is calibrated for multiple subgroups of players. As a concrete use case, we show that (1) the standard biased xG model underestimates Messi's GAX by 17% and (2) Messi's GAX is 27% higher than the typical elite high-shot-volume attacker, indicating that Messi is even a more exceptional finisher than people commonly believed.

cs.LG↗

arXiv2026

Machine Learning and ARIMA Model Averaging for Adaptive Public Health Forecasting: Comparative Evaluation and an Ontario COVID-19 Case Study

Public health forecasts must respond to abrupt changes in surveillance data without over-extrapolating noise, reporting artifacts, or temporary trends. We evaluated autoregressive integrated moving average (ARIMA), random forest, and extreme gradient boosting (XGBoost) models using 190 weekly observations of publicly available Ontario COVID-19 case counts from January 2020 to October 2023. Rolling-origin time-series cross-validation preserved temporal order during model tuning and evaluation. Performance was assessed across three operating dimensions: responsiveness following selected turning points, forecast horizons of one to six weeks, and the amount of historical training data. We also developed Machine Learning and ARIMA Model Averaging (MLAMA), a non-negative performance-weighted ensemble with weights that vary by forecast horizon and responsiveness setting. Retrospective comparisons showed that ARIMA adapted rapidly after turning points but its normalized error increased at longer horizons. Random forest and XGBoost were less responsive initially but maintained more stable normalized error over longer horizons. For two-week forecasts at the end of the study period, training on the most recent data outperformed using longer historical periods, particularly for XGBoost. MLAMA achieved the lowest normalized mean absolute percentage error across most forecast horizons and ranked among the best-performing methods across responsiveness settings. These findings support selecting forecasting models according to operating conditions rather than relying on a single universally preferred approach. MLAMA provides a practical framework for combining complementary statistical and machine-learning forecasts. The accompanying Python package is currently maintained in a private repository while software validation and reproducibility testing are completed.

cs.LG↗

arXiv2026

Reference-Distribution Dependence in LLM-Based Synthetic Persona Data: Diagnosis and Post Hoc Adjustment of Demographic Distributions

We diagnose how closely the demographic distributions in LLM-based synthetic persona data match external reference distributions. For the three variables examined, we show that most of the observed error is attributable to the choice of reference rather than to the generator. Using total variation distance (TVD), we compare the sex x age group x province joint distribution of 1,000,000 records from Nemotron-Personas-Korea (NPK) with Korean official statistics. Against resident-registration figures for April 2026, the time of use, the bias bound, defined as the largest possible difference in the share of any subgroup formed from the three variables, is 1.81 percentage points. This is comparable to the margin of error of a survey of roughly 2,900 respondents. This value is not a fixed property of the data. Matching the reference period and series to the generating reference identified here, the 2024 register-based census restricted to Korean nationals, lowers it to 0.56 percentage points. Over the 15 months between the best-matching month (January 2025) and the time of use, the resident-registration population structure itself moves more than twice the distance of NPK's minimum error. Raking and cell post-stratification, the two weighting schemes used in Korean survey practice, remove most of the reference-period dependence at a variance inflation of about 0.2% in both cases. After raking against the generating reference, the residual joint discrepancy lies at, and marginally above, the upper bound of what a perfect generator would produce when realizing 1,000,000 records (97.6th percentile of the Monte Carlo distribution). We recommend treating synthetic persona data as auxiliary material for small-scale survey design rather than as a substitute for survey data, and re-running both diagnosis and adjustment against official statistics current at the time of use.

cs.CY↗

arXiv2026

IndicQE-APE: A Benchmark for Quality Estimation and Automatic Post-Editing for Indic Languages

Indic quality estimation (QE) and automatic post-editing (APE) data is spread across separate releases, so no single resource supports training and evaluation across tasks and language pairs on one footing. We consolidate the WMT 2020--2024 shared-task lineage with an extended English--Malayalam resource into \indicqe: $126{,}754$ instances over nine directional pairs, with up to four label types aligned on the same segment, a direct assessment, a human post-edit, word-level OK/BAD tags and an error explanation, and a test set stratified over four difficulty axes. On it we benchmark six prompted LLMs and three COMET metrics on segment-level QE, and three systems on APE. Two of the axes are defined partly on the direct assessment and select a compressed slice of it, so each axis is compared against a control drawn from the same language pair with the same score distribution. Only one survives that control: segments whose holistic and token-level quality signals conflict are ranked worse than equally-scored segments of the same language, for all nine systems and all seven pairs that carry the axis. Annotator disagreement, which looks second-hardest without the control, has no effect with it. Few-shot prompting costs every model $\leq$ $3.4$B both correlation and output-format compliance. Within-language accuracy does not make scores comparable across pairs: of the three trained metrics, the one with the best within-language correlation loses most when the pairs are pooled. The benchmark (https://huggingface.co/datasets/surrey-nlp/IndicQE-APE) and code (https://github.com/surrey-nlp/IndicQE-APE) are released.

cs.CL↗

arXiv2026

Measuring the Installed Base: Nordic Health Dataset Catalogues Against HealthDCAT-AP Release 7

The European Health Data Space requires member states to publish machine readable descriptions of the health datasets available for secondary use, and the European Commission publishes HealthDCAT-AP as the metadata profile those descriptions are meant to satisfy. The profile has been designed and validated against curated examples, never against the catalogues already live. We report that measurement for the Nordic region. On 25 August 2026 the 11 Nordic national catalogues harvested by the European data portal held 2,811 dataset descriptions carrying the EU health theme, and none satisfies all eight properties HealthDCAT-AP Release 7 makes mandatory on a dataset. Three of the eight are present on exactly zero records across five countries. Set beside the portal's own quality assessment, which validates DCAT-AP and never mentions the health profile, this is not a health extension skipped on top of sound generic practice: no Nordic catalogue reaches the assessment's top rating band, 5 of the 11 are reported at zero per cent DCAT-AP compliant, and the properties surviving in both layers are the ones a human types into a form, not the ones needing a value bound to a controlled vocabulary. Two further results follow. Finland contributes 2,259 descriptions to the European portal of which 1,146 carry a theme, and not one uses the EU theme authority vocabulary, so a European health filter returns no Finnish dataset at all. Separately, the authority namespace answers HTTP 200 with a well formed empty document for terms it never defined, letting 1,238 datasets across the wider portal carry theme IRIs that resolve to nothing while passing any status code check. We publish the vocabulary, the shapes and the harvesters, record every verdict as a dated observation rather than a property of the dataset, and report the five errors this discipline caught before publication.

cs.DL↗

arXiv2026

Network-Aware Forecasting on Wireless Access Points

Enterprise wireless access points (APs) are promising platforms for predictive machine learning (ML), but their primary responsibility remains providing wireless connectivity and network services. Predictive inference must therefore share an AP's CPU and memory with packet processing, Wi-Fi and IoT radio operations, and client management. This resource contention creates two risks: a model that performs well on proxy hardware may be too slow on the target AP, while a model that fits in isolation may still degrade network services under load. We define \textit{network-aware deployability} using two gates: qualification of the model and its execution path on the target AP, followed by validation of its execution profile under packet-service and forecasting constraints. Our benchmarks show that edge testbeds do not reliably capture target behavior. Across matched artifacts and serving settings, five model implementations run 6.1--19.1$\times$ slower on an AP than on a Raspberry Pi~5, while peak memory usage differs by up to 22\%. Moreover, two forecasting foundation models of similar size differ in AP latency by 19$\times$. When serving a smaller model across 13 parallel streams at a 30~s cadence under network saturation, default execution increases p99 round-trip time (RTT) by 76\% and reduces throughput by 7.06\%. Understanding these trade-offs is essential for live deployment if we aim to use APs for both networking and ML workloads.

cs.NI↗

arXiv2025

Turing complete Navier-Stokes steady states via cosymplectic geometry

In this article, we construct stationary solutions to the Navier-Stokes equations on certain Riemannian $3$-manifolds that exhibit Turing completeness, in the sense that they are capable of performing universal computation. This universality arises on manifolds admitting nonvanishing harmonic 1-forms, thus showing that computational universality is not obstructed by viscosity, provided the underlying geometry satisfies a mild cohomological condition. The proof makes use of a correspondence between nonvanishing harmonic $1$-forms and cosymplectic geometry, which extends the classical correspondence between Beltrami fields and Reeb flows on contact manifolds.

math.DG↗

arXiv2024

The Ramshaw-Mesina Hybrid Algorithm applied to the Navier Stokes Equations

In 1991, Ramshaw and Mesina proposed a novel synthesis of penalty methods and artificial compression methods. When the two were balanced they found the combination was 3-4 orders more accurate than either alone. This report begins the study of their interesting method applied to the Navier-Stokes equations. We perform stability analysis, semi-discrete error analysis, and tests of the algorithm. Although most of the results for implicit time discretizations of our numerical tests comply with theirs for explicit time discretizations, the behavior in damping pressure oscillations and violations of incompressibility are different from their findings and our heuristic analysis.

math.NA↗

arXiv2026

Two Adjoint Perspectives on Fokker-Planck Optimization: A Microscopic-Macroscopic Correspondence

The Fokker-Planck equation admits both a macroscopic Eulerian description through probability densities and a microscopic Lagrangian description through stochastic trajectories. Consequently, optimization problems constrained by the Fokker-Planck equation can be formulated from either perspective. Surprisingly, the corresponding adjoint equations appear to be fundamentally different: the macroscopic adjoint is governed by the backward Kolmogorov equation, whereas the microscopic adjoint evolves pathwise along stochastic trajectories. In this note, we reconcile these two formulations by establishing their correspondence in the continuum setting. We further show that, although their discrete gradients no longer coincide after discretization, both provide consistent numerical approximations of the continuum gradient. Explicit convergence rates are established for both discretization strategies.

math.NA↗

arXiv2026

Variable-Granularity Tokenization for High-Resolution Object Detection

ViT detectors fix a uniform token grid before any learned stage. A native-resolution aerial detector must then choose between resolving few-pixel objects and staying inside compute and memory limits. We introduce VGTok, a training-free tokenizer that sets patch granularity per region from pixels, ahead of the encoder. VGTok scores each region by multi-scale morphological top-hat separability from its surround, then thresholds those scores at a per-image percentile, which fixes the token budget. A structure-tensor gate ($λ_{\min}$) refines only where two-dimensional object structure supports it, leaving one-dimensional clutter coarse. The resulting token set is a strict partition of the image. In a Co-DETR detector with an EVA-02 ViT-L encoder, VGTok clears every published VisDrone-val AP and AP$_S$ at every budget from 40\% to 100\% of tokens. At 40\% it records 44.22 AP with three fifths of the sequence discarded before the first transformer block; dense, it reaches 48.38 AP, $6.08$ above the strongest published entry. VGTok transfers to AI-TOD-v2 untouched, same scorer and same rank, and sets a new state of the art at 37.27 AP and 19.51 AP$_{vt}$. As a pure drop-in into a frozen checkpoint it reaches 36.29 AP at 78.5\% of tokens, above every published entry, where our 376.3M-parameter detector clears a 3.0B multi-expert model. We show that a token budget fixed before the backbone, from local separability and structure geometry alone, holds accuracy on the tiny-object regimes that dominate aerial detection, at $3.1\times$ less encoder compute and $1.9\times$ less encoder memory. Code and models are available at \href{https://github.com/khayrulbuet13/vgtok}{\texttt{github.com/khayrulbuet13/vgtok}} and \href{https://huggingface.co/khayrulbuet13/vgtok}{\texttt{huggingface.co/khayrulbuet13/vgtok}}.

cs.CV↗

arXiv2026

Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees

Uncertainty quantification for partial differential equations is traditionally grounded in discretization theory, where solution error is controlled via mesh/grid refinement. Physics-informed neural networks fundamentally depart from this paradigm: they approximate solutions by minimizing residual losses at collocation points, introducing new sources of error arising from optimization, sampling, representation, and overfitting. As a result, the generalization error in the solution space remains an open problem. Our main theoretical contribution establishes generalization bounds that connect residual control to solution-space error. We prove that when neural approximations lie in a compact subset of the solution space, vanishing residual error guarantees convergence to the true solution. We derive deterministic and probabilistic convergence results and provide certified generalization bounds translating residual, boundary, and initial errors into explicit solution error guarantees.

cs.LG↗

arXiv2026

A multi-class kinetic traffic flow model: discrete-velocity formulation and diffusively-corrected macroscopic limits

This paper introduces a multi-class extension of a discrete-velocity kinetic traffic flow model based on a non-local Prigogine-Herman framework. We derive a hyperbolically scaled system of equations from a continuous kinetic formulation describing interactions between different vehicle classes through braking and relaxation terms. The model is then discretized with respect to the velocity variable for an arbitrary number of vehicle classes, and the structural properties of the resulting formulation are analyzed. In particular, we prove hyperbolicity and total linear degeneracy. Due to the non-conservative structure of the model, we employ a path-conservative finite volume scheme for the numerical approximation of the system. Finally, we derive the corresponding diffusively-corrected macroscopic multi-class model, investigate its stability and present numerical simulations on a single-lane road to illustrate the theoretical findings.

math.NA↗

arXiv2026

Optimal error estimates for the half-way bounce-back lattice Boltzmann method for the Stokes equations

We give a mathematical proof of the optimal convergence rates for the D2Q9 BGK lattice Boltzmann method with the half-way bounce-back rule for the incompressible Stokes equations in a flat channel. The convergence rates are second-order for the velocity and first-order for the pressure as the lattice spacing $h$ tends to zero, in agreement with formal analyses and numerical experiments, whereas the available rigorous convergence theorems only yield an $O(h^{1/2})$ bound for the velocity error. A key step in the proof is a decomposition of the leading boundary consistency error into macroscopic and kinetic components. These components are absorbed by suitably constructed Stokes and discrete Knudsen layer correctors, respectively. Incorporating these correctors into the prediction function used in previous rigorous analyses, we obtain a refined prediction function with consistency errors of sufficiently high order. Combined with the known weighted $L^2$-stability estimate, this gives the optimal convergence rates.

math.NA↗

arXiv2026

A Variational Method for Conformable Fractional Equations Using Rank-One Updates

We make a complete variational treatment of rank-one Proper Generalised Decomposition for separable fractional partial differential equations with conformable derivatives. The setting is Hilbertian, the energy is induced by a symmetric coercive bilinear form, and the residual is placed in the dual space. A greedy rank-one update is obtained by maximizing an energy Rayleigh quotient over the rank-one manifold, followed by an exact line search. An exact one step energy decrease identity is proved, together with geometric decay of the energy error under a weak greedy condition that measures how well the search captures the Riesz representer of the residual. The alternating least squares realization is analyzed at the level of operators, including well posedness of the alternating subproblems, a characterization of stationary points, and monotonicity of the Rayleigh quotient along the inner iteration. Discretizations based on weighted finite elements and on Grünwald type schemes are described in detail, including assembly, boundary conditions, complexity, and memory. Two model problems, a stationary fractional Poisson problem and a space time fractional diffusion problem, are treated from the continuous level down to matrices.

math.NA↗

arXiv2026

Well-posedness and numerical reconstruction of a source term for linear parabolic problems with an integral constraint

This work investigates a time-dependent source identification problem for linear parabolic equations subject to an integral constraint and Neumann boundary conditions in a domain of $\mathbb{R}^d$, $d\ge 1$. We establish well-posedness and higher regularity of the solution pair in parabolic Hölder spaces. A numerical algorithm based on a finite element discretization in space and an implicit time-stepping scheme is then developed for the reconstruction of the unknown source. The resulting discrete inverse problem involves a well-conditioned operator. We show that identity Tikhonov regularization provides only uniform, nonselective shrinkage in this setting, whereas Tikhonov regularization with derivative-based penalties, analyzed through the generalized singular value decomposition, provides an effective denoising strategy. The regularization parameter is selected using the Morozov discrepancy principle. Numerical errors are evaluated using full parabolic Hölder norms, which provide a more comprehensive assessment of the reconstruction by incorporating errors in the solution, its derivatives, and the associated Hölder seminorms. Numerical experiments for smooth and piecewise constant sources demonstrate accurate and robust reconstructions under increasing levels of noise.

math.AP↗

arXiv2026

Sharp Mixed Spectral Barron Regularity of Coulombic Many-Electron Wave Functions

We establish sharp mixed spectral Barron regularity for eigenfunctions of molecular Coulomb Hamiltonians. The mixed norm is a Fourier $L^1$ norm with one isotropic weight and coordinate-product weights, and therefore detects regularity invisible to the isotropic Barron scale. For a nonempty set $I$ of electron indices on which the wave function is antisymmetric, we derive an explicit admissible region for the isotropic order $s$ and the coordinate orders $α,β$. This region is optimal as a uniform statement over the class of clamped-nuclei Coulomb Hamiltonians. For fixed-spin components with two occupied spin blocks, it reduces to $s+α+β<1$; in the fully spin-polarized class it reduces to $s+α<1$. In particular, if $\mathcal I_σ$ denotes the family of occupied same-spin blocks determined by $σ$, then every fixed-spin spatial component $ψ_σ$ satisfies, for every $0\leqα<1$, \[ \left(\sum_{I\in\mathcal I_σ}\prod_{i\in I}\langleξ_i\rangle^α\right)\widehat{ψ_σ}\in L^1(\mathbb{R}^{3N}). \] For a fully spin-polarized state, $\mathcal I_σ=\{\{1,\ldots,N\}\}$.

math.AP↗