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arXiv2026

Multilingual Lexical Feature Analysis of Spoken Language for Predicting Major Depression Symptom Severity

Background: Remotely captured spoken language could provide objective, regular indicators of depression symptom severity. However, research to date has largely used non-clinical, cross-sectional written language and complex machine learning (ML) approaches with limited interpretability. Methods: We used linear mixed-effect models to identify interpretable lexical features associated with symptom severity in data from the RADAR-MDD study that comprised 5,846 smartphone recordings and Patient Health Questionnaire (PHQ-8) scores from 467 participants in the UK, Netherlands and Spain. We then developed ML models and systematically assessed via nested cross-validation whether interpretable lexical features or high-dimensional vector embeddings improved the accuracy of PHQ-8 prediction over sociodemographic and confounding features. Results: Depression symptom severity was associated with five lexical features, including reductions in word count measures, use of first-person plural pronouns and positive word frequency. Associations were stable across countries, except for positive word frequency. Lexical features and vector embeddings did improve prediction accuracy beyond baseline models. Limitations: Our cohort was skewed in age (median = 53, IQR 35 to 62) and majority female (n=357), potentially affecting the generalizability of our results. A lack of natural language processing tools for non-English languages restricted our feature choices. Conclusion: Further research is required to realise the value of spoken lexical markers in clinical research and practice including larger and more diverse samples, elicitation protocol development and analytical methods that account for within- and between-individual variations.

cs.CL↗

arXiv2026

A Barrier-Regularized Symmetric Nitsche Method for the Signorini Problem

We introduce and analyze a barrier-regularized symmetric Nitsche method for the scalar Signorini problem. Applying a logarithmic barrier to the nonnegative slack variable in an augmented Lagrangian and then eliminating that variable yields a smooth positive-part operator and the perturbed complementarity relation on a primal-dual central path, with barrier parameter $μ=γs$. For every $s>0$, the discrete problem is continuously differentiable, uniquely solvable, and has a symmetric positive definite Newton matrix when the Nitsche parameter is sufficiently large. Under a mild barrier-feasibility condition, the continuous logarithmic energy has a unique minimizer $u_μ$ for every $μ>0$, its gap is positive almost everywhere, and $\|u-u_μ\|_{H^1(Ω)}\lesssimμ^{1/2}$. Under the Sobolev regularity used for finite element approximation, this minimizer satisfies the $L^2$ central-path boundary law. If the obstacle is locally the trace of an $H^2$-function, we also prove a uniform local $H^2$ bound in the interior of each planar contact face, on neighborhoods that may contain a free-boundary point of the limiting Signorini solution. The method is exactly consistent and quasi-optimal relative to $u_μ$, with constants independent of $s$. If $u_μ$ is uniformly bounded in $H^r(Ω)$, $3/2<r\leq k+1$, then $\|u-u_h\|_{H^1(Ω)}\lesssim h^{r-1}\|u_μ\|_{H^r(Ω)}+μ^{1/2}$; hence the sufficient balance $s\lesssim h^{2r-1}$ preserves the available energy-norm rate. We also derive rates for discrete penetration and the complementarity residual. Numerical experiments with $P_1$ and $P_2$ elements on structured and unstructured meshes support the predicted rates and the local Newton theory, while showing that a rate-preserving smoothing may still resolve the contact set poorly.

math.NA↗

arXiv2026

Beyond Reproducibility: Token Probabilities Expose Large Language Model Nondeterminism

The execution of Large Language Models (LLMs) has been shown to produce nondeterministic results when run on Graphics Processing Units (GPUs), even when they are configured to produce deterministic results. This is due to the finite precision effects of the arithmetic operations, which depend on the order in which they are executed. This order, in turn, depends on the processes that are running concurrently on the GPU. Previous studies have focused on the impact of nondeterminism on the text generated by the LLMs or on proposing mechanisms to achieve deterministic execution. This work takes a closer look at nondeterminism by analyzing the variations on the token probabilities, not on the generated text. Interestingly, all the models evaluated have similar results in both the trends and the actual values of the variations of the probabilities. In particular, the results show that the effects of nondeterminism are significant for token probabilities that are in the range of 0.1 to 0.9, while they are much smaller when the probabilities are close to 0 or 1. This has significant implications for our understanding of nondeterminism. The first is that nondeterminism will likely have a non-negligible impact on generated text when the temperature is not zero, as it introduces significant variations in the token probabilities except when they are close to 0 or 1. Secondly, it suggests that all models have similar non deterministic variations at the token probability level. Therefore, different variations in the performance of the generated text, for example, when measuring accuracy on a benchmark, seem to come from different token probabilities or response lengths. A third implication is that we may be able to estimate the impact of nondeterminism by running a single inference and analyzing the token level probabilities, instead of having to run the same inference many times.

cs.AI↗

arXiv2026

Adaptive multigrid for high-order discontinuous Galerkin methods based on the full approximation scheme

We propose an adaptive multigrid (MG) method for discontinuous Galerkin formulations of elliptic problems using Brandt's full approximation scheme (FAS). Unlike common approaches, this method achieves local $hp$-refinement of hexahedral meshes without the need for hanging nodes. The core component of the FAS-MG method is an overlapping Schwarz smoother, which is optionally accelerated by a Krylov method. This smoother is designed for unstructured curvilinear meshes but maintains a tensor-product structure for fast diagonalization. Numerical experiments demonstrate the exceptional efficiency of the FAS-MG method. Dedicated studies confirm its robustness against high aspect ratios, element deformation, and irregular mesh topology. We also verify its capability for dynamic parallel mesh adaptation using the wave-front benchmark of Červený, Dobrev, and Kolev (SIAM J. Sci. Comp. 41, 2019). Finally, we present preliminary results of extending the method to incompressible Navier-Stokes problems.

math.NA↗

arXiv2026

On the differential of the exponential map

We study the time derivative of the matrix exponential $B(t)=\mathrm{exp}(A(t))$, where $A(t)$ is a time-parametrized curve in $\mathrm{Mat}(n)$. Starting from the Taylor series expansion, we derive a nested summation formula, which is then reformulated into a double summation. This expression is converted into an integral representation using Euler's beta function, and further expressed in terms of Lie brackets and the adjoint representation. Later, we extend this to a family of problems and verify a well-known result. Finally, we establish connections to the Gateaux and Fréchet derivatives, proving the latter's existence. These results offer a unified and explicit framework for understanding the derivative of the exponential map.

eess.SY↗

arXiv2026

SPARK: Skeleton-Guided Reasoning Synthesis from Large-Scale Scientific Literature

Scientific reasoning remains challenging for open-source models, largely due to the lack of high-quality scientific reasoning data. Existing datasets are often dominated by factual recall or formulaic problem solving, with limited emphasis on mechanism understanding, evidence-grounded reasoning, and hypothesis evaluation. To address this, we introduce SPARK (Scientific Paper Abstracted Reasoning sKeleton), a paper-oriented synthesis framework built on Sci-Base, a large-scale corpus of research papers spanning 10 scientific disciplines. Instead of directly converting papers into question-answer pairs, SPARK treats the claim-evidence-derivation structure of a paper as the fundamental unit of reasoning synthesis. Specifically, SPARK (1) distills each paper into a compact reasoning skeleton capturing its central claims and supporting evidence, enabling self-contained question generation, and (2) synthesizes reasoning tasks from four scientific perspectives: mechanistic reasoning, hypothesis falsification, quantitative derivation, and boundary calibration. A final consistency verification stage further removes unsupported or contradictory outputs. Using this framework, we construct Spark-234K, a scientific reasoning dataset with substantially higher difficulty and diversity than existing resources. Experiments show that Spark-234K consistently outperforms existing scientific reasoning datasets while achieving stronger performance with significantly fewer training samples.

cs.AI↗

arXiv2026

LitCurate: A Configuration-Driven AI-Assisted Framework for Scientific Database Construction with an Application to Lower-Mantle Equation-of-State Data

The growing scientific literature contains decades of experimental and computational results that could support data-driven and physics-based modeling, yet much of this infor- mation remains locked in publications and is not readily usable for large-scale analysis or sci- entific software. Building structured databases from the literature is particularly challenging whenrelevantstudiesmustfirstbediscoveredamonglargecollectionsofpapersandreported quantities must be extracted with enough scientific context to remain usable. We present LitCurate, an open-source framework for building scientific databases from the literature using large language models within an auditable, stage-wise curation workflow. LitCurate integratesliteraturediscovery, relevancescreening, full-textprocessing, andstructuredinfor- mation extraction while retaining intermediate results and provenance, allowing researchers to inspect and revise individual stages rather than treating automated curation as a black- box process. We apply LitCurate to construct an equation-of-state database of lower-mantle and lower-mantle-relevant high-pressure mineral phases from experimental and theoretical studies, comprising 1,334 entries from 205 papers. The resulting dataset links reported equation-of-state parameters to mineral phases, compositions, equation formulations, meth- ods, and parameter constraints, and labels values as source-reported or citation-reported when provenance can be determined. The records are available through a searchable web application. By connecting scientific literature to traceable, machine-readable data, LitCu- rate provides a reusable approach for transforming accumulated literature into resources for scientific analysis and computational modeling.

cs.IR↗

arXiv2026

Integral Invariants of Vasudeva Murthy's Relaxation Systems: Analysis and Numerical Validation

Vasudeva Murthy's relaxation approach [A.S. Vasudeva Murthy, J. Comput. Appl. Math., 203(2), pp. 437-443, 2007], originally proposed for the Jin-Xin relaxation model, provides an alternative formulation with invariant properties that is consistent and retains the semilinear structure incomparison to the standard one. In this work, Vasudeva Murthy's relaxation approach for various relaxation systems are proposed such as the shallow water equations, the Broadwell model, the Euler equations with heat transfer and two-dimensional Jin-Xin model. For proposed relaxation models, the associated integral invariants are rigorously established at the theoretical level. The main advantage of the integral invariant is that it provides a conserved quantity for the relaxation system by incorporating the coupled contributions of the solution variables in vector form. To validate the analytical results, numerical simulations are carried out for each model using three second-order numerical schemes: CS-EBT2, a semi-implicit second-order central finite-volume scheme for hyperbolic systems with relaxation source terms [S. Sahu, E. Macca, and R. Samala, J. Comput. Phys., 563, 115100, 2026]; UCS2, a finite-volume central relaxation-type scheme [S. F. Liotta, V. Romano, and G. Russo, SIAM J. Numer. Anal., 38(4), 1337-1356, 2000]; and IMEX-RK2, a second-order Implicit-Explicit Runge-Kutta scheme [Pareschi and Russo, J. Sci. Comput., 25, 129-155, 2005]. Numerical results, compared to exact or finely resolved reference solutions, confirm that the models preserve integral invariants, remain stable under CFL restrictions, and exhibit robust and accurate behavior across all benchmark systems tested.

math.NA↗

arXiv2026

Spectral Features Dominate BCG Respiratory-Event Detection: A Large-Scale Patient-Independent Comparison of Feature Groups in Sleep Apnea Patients

Unobtrusive ballistocardiographic (BCG) sensing is a promising modality for long-term sleep-apnea monitoring, yet it remains unclear which signal features are most discriminative for respiratory-event detection. We present a literature-guided, patient-independent comparison of ten BCG feature groups using a 512-sensor capacitive pressure mat recorded simultaneously with respiratory polygraphy in 155 patients (52 female, 103 male) undergoing in-hospital evaluation for obstructive sleep apnea. Features were extracted from six spatially distinct signal channels, yielding a 191-dimensional feature vector spanning general statistical, time-domain, frequency-domain, wavelet, frame-energy, and nonlinear complexity descriptors. Under strict leave-one-patient-out cross-validation for binary classification of respiratory-event windows versus event-free reference windows, Random Forest and Histogram Gradient Boosting achieved AUC-ROC of 0.967 and 0.969 and AUC-PR of 0.977 and 0.979, respectively. Feature-importance analysis revealed that frequency-domain features dominate discrimination: breathing-band power in the 0.1-0.4 Hz range accounted for 30.3% of total discriminative information across all spatial channels, and Fast Fourier Transform spectral-shape descriptors of the adaptively preprocessed channel contributed a further 15.1%. AUC and curve-length features provided the main complementary time-domain evidence (21.5%), whereas wavelet-derived and nonlinear features contributed smaller secondary effects (10.4% combined across 59 features). Frequency-domain and time-domain features together accounted for 67% of total discriminative information, demonstrating that a compact, interpretable subset of the full feature library achieves clinically relevant performance under patient-independent validation and providing an empirical basis for feature selection in future BCG systems.

cs.LG↗