## 1 Introduction  
With an increasing number of individuals over 65 years of age around the world, an increasing number of people face functional impairments associated with aging, including reduced balance function and increased fall risk [1]. Nearly 30% of older adults report falling [2], which leads to injuries, reductions in quality of life, and even death [2, 3, 4]. Considering the severe consequences of falls in older adults, it is essential to further our understanding of the mechanisms underlying falls and the evaluation of factors that may contribute to the effectiveness of training programs aimed at reducing falls in older adults. Postural control [5] declines with advancing age and is strongly associated with an increased fall risk in older adults [6]. Postural control is defined as the act of maintaining, achieving, or restoring a state of balance that may involve either a fixed-support or a change in support response [7]. Postural control is commonly assessed using posturography, which quantitatively evaluates postural stability [5]. Compared to younger adults, older adults show significantly reduced performance under sway-referenced surface conditions when visual input is absent or unavailable, suggesting age-related declines in vestibular function and overall balance control [8]. This impairment is even more pronounced in older adults at higher risk of falling, who demonstrate a reduced ability to rely on vestibular input when both visual and somatosensory information are inaccurate [5; 8; 9]. Similarly, a study on older women found diminished stability under these conditions, along with an age-related decline in somatosensory function. These findings point to a general deterioration of both somatosensory and vestibular systems with age and emphasize the growing compensatory importance of visual input in maintaining balance [10]. Nonetheless, further research is needed to assess the effectiveness of targeted, evidence-based interventions, such as Tai Chi, for improving postural control and reducing fall risk in older adults [11]. Tai Chi is a Chinese martial art that combines physical practice, breathing techniques, and meditation, which has been widely used to improve postural control and prevent falls in older adults [11; 12; 13]. Prior work has demonstrated the effectiveness of Tai Chi at improving postural control [14]. Specifically, Tai Chi practitioners have exhibited greater postural stability by reducing their reliance on perturbed visual or proprioceptive inputs while relying more on unperturbed visual, proprioceptive, or vestibular inputs under various sensory perturbation conditions [15]. However, there have been ambiguous findings on the exact mechanism that may be underlying Tai Chi practice benefits in postural control [16]. Upright postural and balance control requires a complex interplay within and between the sensory and the motor systems. Furthermore, there is strong evidence for the crucial contribution of the cerebral cortex in the control of balance [17; 18; 19]. The variability of the center of pressure (COP) in postural control can be decomposed into two main components: rambling and trembling [20; 21]. Rambling reflects the movement of a reference point, which estimates the body's dynamic state and is formed through the integration of various sensory inputs [22]. Trembling consists of high-frequency oscillations around the reference point, primarily regulated by the intrinsic stiffness of muscles and spinal reflexes [20; 21]. In line with the work performed by [PERSON] et al. [23], rambling is defined as the trajectory of the COP at instantaneous equilibrium points (IEPs)--the moments when the horizontal ground reaction force is zero. At these points, the body's position is considered to be in mechanical equilibrium, and the COP at IEPs effectively reconstructs the voluntary, low-frequency component of postural control. As a result, the rambling trajectory closely resembles the original COP time series, capturing the overall movement path of the body's center of mass.