From Pen Strokes to Sleep States: Detecting Low-Recovery Days Using Sigma-Lognormal Handwriting Features

Digital handwriting acquisition enables the capture of detailed temporal and kinematic signals reflecting the motor processes underlying writing behavior. While handwriting analysis has been extensively explored in clinical or adult populations, its potential for studying developmental and educational characteristics in children remains less investigated. In this work, we examine whether handwriting dynamics encode information related to student characteristics using a large-scale online dataset collected from Japanese students from elementary school to junior high school. We systematically compare three families of handwriting-derived features: basic statistical descriptors of kinematic signals, entropy-based measures of variability, and parameters obtained from the sigma-lognormal model. Although the dataset contains dense stroke-level recordings, features are aggregated at the student level to enable a controlled comparison between representations. These features are evaluated across three prediction tasks: grade prediction, gender classification, and academic performance classification, using Linear or Logistic Regression and Random Forest models under consistent experimental settings. The results show that handwriting dynamics contain measurable signals related to developmental stage and individual differences, especially for the grade prediction task. These findings highlight the potential of kinematic handwriting analysis and confirm that through their development, children's handwriting evolves toward a lognormal motor organization.

Recovering online pen trajectories from offline handwriting images, often referred to as handwriting trajectory recovery (stroke recovery), is an offline-to-online conversion task with applications in stroke-level editing and forensic analysis. We propose, to the best of our knowledge, the first diffusion-model-based framework for this task. Our method formulates trajectory recovery as image-conditioned generation and uses a denoising diffusion model to sample pen trajectories consistent with the observed ink trace. Through extensive quantitative evaluations on CASIA-OLHWDB (1.0-1.1), we verify that the proposed approach enables accurate recovery even for complex multi-stroke characters, substantially improving both temporal similarity (DTW/LDTW) and shape fidelity (AIoU) over representative prior methods such as PEN-Net and Cross-VAE. We further show that the model captures general stroke-order tendencies and generalizes to classes unseen during training, exemplified by cross-script transfer: a model trained on Chinese characters can recover reasonable stroke orders for Latin letters to some extent.

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.