Riemannian Stochastic Gradient Method for Nested Composition Optimization

This work considers optimization of composition of functions in a nested form over Riemannian manifolds where each function contains an expectation. This type of problems is gaining popularity in applications such as policy evaluation in reinforcement learning or model customization in meta-learning. The standard Riemannian stochastic gradient methods for non-compositional optimization cannot be directly applied as stochastic approximation of inner functions create bias in the gradients of the outer functions. For two-level composition optimization, we present a Riemannian Stochastic Composition Gradient Descent (R-SCGD) method that finds an approximate stationary point, with expected squared Riemannian gradient smaller than $\epsilon$, in $O(\epsilon^{-2})$ calls to the stochastic gradient oracle of the outer function and stochastic function and gradient oracles of the inner function. Furthermore, we generalize the R-SCGD algorithms for problems with multi-level nested compositional structures, with the same complexity of $O(\epsilon^{-2})$ for the first-order stochastic oracle. Finally, the performance of the R-SCGD method is numerically evaluated over a policy evaluation problem in reinforcement learning

COULD TAI CHI EXERCISE IMPOVE STABILITY IN ELDERLY? STRATEGIES OF STEPPING OVER OBSTACLES

Stepping over obstacles challenges stability and is a leading cause of falls in older adult populations. The purpose of this study was to evaluate the obstacle-crossing strategies of long-term Tai Chi (TC) practitioners and exercise walkers. Thirty healthy older women (average age: 65.7 years) with either TC (n=15) experience (average experience: 8.2 years) or walking exercise (n=15; average experience: 8.8 years) participated in this study. We used three trial conditions: 1) normal walking, 2) crossing a 15cm (20% of leg length) obstacle, and 3) crossing a 23cm (30% of leg length) to assess obstacle-crossing strategy. Results showed Individuals with a TC background crossed the obstacle significantly faster with a significantly longer step relative to the exercise walkers; plantar pressure profiles between the two groups also differed. Our results suggest that obstacle-crossing strategies were affected by the type of long-term exercise

EFFECTS OF EXERCISE ON ANKLE PROPRIOCEPTION DURING SIXTEEN WEEKS OF TRAINING AND EIGHT WEEKS OF DETRAINING IN OLDER ADULTS

This study evaluates the ankle proprioception in older adults. Sixty women (age 62.1±4.3yr) were randomly assigned to three groups to undergo a 16-week training (one group practice Tai Chi,one group practice brisk walking and one group reading) and 8-week detraining program. Proprioception of ankle plantarflexion (PF), dorsiflexion (DF) were measured, better proprioception is defined as being able to detect a smaller degree in joint angle. The results showed that degree PF and DF changes earlier and were smaller in TG than in BG in training; degree of PF and DF declined in all groups during the detraining, but TG exhibited a significant difference with pre-training data. So Tai Chi can more effectively improve and maintain ankle proprioception as well as prevent fall in old age. However, the extent of benefit depends on the regularity of training in older adults

The RELIABILITY OF A NEW DEVICE FOR ASSESSING ANKLE JOINT PRORIOCEPTION IN HEALTHY ADULTS

The objective of this study is to evaluate the within-day and between-day reliability of a new device for assessing ankle joint prorioception. Eleven healthy adults, composed of seven males and four females, participated in the study. Each subject completed three sessions, two on the same day and the last one week later. In each session, three successful testing trials for ankle joint plantarflexion, dosiflexion, inversion, and eversion were performed. The mean values in one direction were calculated and analyzed. The within-day ICC values ranged from 0.808 to 0.973. The SEM for the device ranged from 0.118 ° to 0.448 °. The between-day ICC values ranged from 0.628 to 0.884. The SEM ranged from 0.287 °to 0.618 °. The measurements indicate good to excellent reliability of the device

EFFECTS OF LONG-TERM TAICHI ON THE STABILITY OF THE ELDERLY DURING STAIR DESCENTS UNDER DIFFERENT ILLUMINATIONS

This study investigates the effectiveness of Tai Chi on the stability of the elderly during stair descents under illumination of 3 lx and 300 lx. A total of 30 healthy elderly who are aged between 65 and 70 years old are recruited as subjects. Two force plates and eight Vicon cameras were used to collect data. The results indicated that Tai Chi exercise may increase the lower limb strength of the elderly, the stair descent strategies was influenced by Intensity of illumination, it may increase the risk of fall during stair descent under lower Intensity of illumination

THE POTENTIAL INJURY RISK OF BACKPACK WEIGHT ON POSTURE AND GROUND REACTION FORCES OF OBESE CHILDREN DURING STAIR DESCENT

This study investigated the effects of backpack weight on posture, gait pattern, and ground reaction forces for children with obesity in an attempt to define a safe backpack weight limit for them. A total of 16 obese (11.19±0.66 years of age) and 21 normal body weight (11.13±0.69 years of age) school boys were recruited. Two force plates and two video cameras were used. Multivariate analysis of variance with repeated measures was employed. Obese children showed increased trunk and head forward inclination angle, increased ground reaction force in the medial-lateral and anterior-posterior directions when compared to male children with a normal body weight. The changes were observed even with an empty backpack in comparison with normal body weight children and a 15% increase in backpack weight led to further instability and damage on their already strained bodies

COULD LONG-TERM EXERCISE IMPROVE THE OBSTACLE-CROSSING ABILITY OF ELDERLY WOMEN? EFFECTS OF TAI CHI AND AEROBIC DANCE EXERCISES

The purpose of this study was to evaluate the effects of long-term exercises (TaiChi (TC), aerobic dance) on the obstacle-crossing ability of elderly women, as well as to identify whether the exercise could considerably improve stability. Forty-five elderly women include TC, aerobic dance and no exercising groups participated in our study. They walked a short distance to cross the obstacle (30% of leg length). Results showed that long-term exercise had a positive effect on muscle strength and the practitioners used an obstacle-crossing strategy that increasing the force in medial–lateral and anterior-posterior directions of the trailing foot to cross obstacle. The TC strategy was better than aerobic dance in improving balance and increasing the height of the leg during obstacle-crossing

EFFECTS OF RUNNING BIOMECHANICS ON THE OCCURRENCE OF ILIOTIBIAL SYNDROME IN MALE RUNNERS — A PROSPECTIVE STUDY

This study aimed to determine the gait characteristics that easily induce ITBS and explore the gait changes after the occurrence of ITBS. 30 healthy male runners participated in our study, 15 in ITBS and control group respectively. All participants underwent two gait trials, namely, before the first day of their routine running and after 8 weeks. After 8 weeks of running, the ITBS group exhibited greater peak anterior pelvic tilt and hip flexion angle than the control group. The ITBS group showed increased peak trunk inclination angle, whereas the control group demonstrated lower peak hip flexion and peak hip adduction than those at the beginning of running. Decreased peak hip flexion and peak hip adduction angle was a gait adjustment strategy that could be used to avoid ITBS occurrence. Excessive trunk posture and pelvic activity during running are also ITBS risk factors