The following three-part proposal will explore the impact of applying motor-cognitive incorporated training (MCIT) in individuals with post-stroke cognitive impairment (PSCI) or Moyamoya disease (MMD), and examine the relationship between cognitive and motor impairments and brain activation patterns in these populations. Part I is a cross-sectional study designed to characterize cognitive and motor performance and their relationship with brain activation patterns in individuals with post-stroke cognitive impairment (PSCI) or Moyamoya disease (MMD), compared to age-matched healthy controls. Thirty participants will be screened for eligibility and recruited for each group (90 participants total). After collecting basic data, all participants will undergo cognitive and motor function tests. Cognitive function tests include tests of global cognition, and executive function. Motor function tests include tests of sensorimotor function, single and dual task standing, muscle strength, and ambulation ability. Functional near-infrared spectroscopy (fNIRS) will be used to evaluate the brain activation during the cognitive tests, and single and dual task standing. Results from all tests will be used to determine the motor, cognitive, and other functional performance, and will be used in the design of the training program in Part II and III. Part II and III are single-blinded randomized controlled trials that will explore the short and long-term effects of a motor-cognitive incorporated training (MCIT) on motor, and cognitive function in individuals with post-stroke cognitive impairment (PSCI) or Moyamoya disease (MMD). 60 individuals with PSCI (Part II), and 60 individuals with MMD (Part III) will be recruited. After screening for eligibility and collection of demographic data, participants will undergo a pretest assessment. In addition to the motor and cognitive tests used in Part I, stroke location, and time of onset will also be collected for each participant. Brain activation will be assessed during the cognitive tests, single and dual task standing assessments using fNIRS. Participants will be randomly allocated to one of the two groups (MCIT group and active control group) (n=30 in each group) via a sealed envelope selected by a blinded assistant. The training protocol is 30 minutes per session, 3 sessions per week for a total of 4 weeks. The control group will receive motor training only, including upper and lower extremity exercises, bed mobility, strengthening (core and extremities), and balance training, progressing from static to dynamic tasks. The MCIT group will engage in the program combines motor and cognitive training that starts with attention and short-term memory tasks, advancing to working memory and inhibitory control with increasing difficulty. A post-test will be conducted after the 4-week intervention, followed by follow-up assessments at 1, 3, and 12 months for individuals with PSCI or MMD in both the control group and the MCIT group. At the 3-month follow-up, participants who are unable to attend in person will be contacted by telephone. At the 12-month follow-up, all participants will receive a telephone interview focused on return-to-work status.