This study identifies new depression biomarkers based on the dynamical properties of tract variables, which represent geometric features describing the configuration of the speech articulators. A key advantage of this approach lies in its ability to quantify aspects of the articulatory process that have not been previously explored in the context of depression, namely predictability, complexity, and randomness. These properties are respectively characterised using the Largest Lyapunov Exponent, the Correlation Dimension, and the Sample Entropy. Thorough experiments were conducted on the Androids Corpus, a publicly available dataset comprising 64 speakers diagnosed with depression by clinicians and 54 control speakers with no reported history of mental health conditions. The results indicate that the proposed biomarkers effectively discriminate between the depressed and control speakers, as evidenced by the high Cliffs delta values across both read and spontaneous speech.
The cardiovascular system evolves along a bounded trajectory in physiological state space that converges to a compact geometric object: the cardiac attractor. A wearable photoplethysmograph (PPG) or electrocardiograph (ECG) observes a one-dimensional projection of this attractor; by Takens' embedding theorem, delay coordinates reconstruct its full geometry. Three decades of nonlinear cardiac dynamics have extracted Lyapunov exponents, recurrence statistics, and sample entropy from reconstructed attractors, yet no principled account exists of which attractor properties capture which cardiovascular quantities, or why, leaving feature selection as a search problem and negative results uninterpretable. We introduce Attractor Domain Theory (ADT), which proves that the reconstructed attractor's information partitions into three mutually non-redundant domains: the Geometry Domain G (delay embedding; native capability: artifact rejection), the Ergodic Domain S (asymptotic statistical invariants; native capability: stability estimation), and the Variational Domain V (finite-time Lyapunov exponent field; native capability: hemodynamic inference). We prove a Domain Sufficiency Theorem (the Parseval analog for attractor information) and establish that three domains are necessary and sufficient. Geometry Domain validation via the SCSI framework across 176,742 PPG segments from four datasets yields AUC = 0.757 [0.686-0.828] and NPV = 0.966 after correcting three systematic evaluation artifacts (+0.179 net inflation). Ablation confirms C_NL as the dominant Geometry Domain component (Delta AUC = -0.413) and intra-domain redundancy across five components.