Here is the design of a clinical trial:

Official Title: Pilot Study Among Type 2 Diabetes Patients Investigating Effects of Computerized Cognitive and Physical Activity Programs Combined or Single.

Included conditions:
- Diabetes Mellitus, Type 2

Study Armgroups:
- {'label': 'Group 1: physical activity then cognitive training', 'type': 'EXPERIMENTAL', 'description': 'Using an online-computerized application, physical activities will be prescribed for one month. After a 15 days break, cognitive training activities will be prescribed the same way. A feedback by the patient will be asked fallowing each activity to control the observance.', 'interventionNames': ['Behavioral: Physical activity', 'Behavioral: cognitive training']}
- {'label': 'Group 2: Cognitive training then physical activity', 'type': 'EXPERIMENTAL', 'description': 'Contrary to the first group, the second one starts with cognitive training intervention then engages in physical activity in same way as the first group. A feedback by the patient will also be asked fallowing each activity to control the observance', 'interventionNames': ['Behavioral: Physical activity', 'Behavioral: cognitive training']}
- {'label': 'Group 3 : resonance frequency breathing then combined physical activity and cognitive training', 'type': 'EXPERIMENTAL', 'description': 'The third group takes part in a 1 month breathing exercise program. After a 15 days break (as the groups 1 and 2), a combined physical activity and cognitive training program is administrated for 1 month. As the others arms, a feedback by the patient will be asked fallowing each activity to control the observance', 'interventionNames': ['Behavioral: combined physical and cognitive training']}

Interventions:
- {'type': 'BEHAVIORAL', 'name': 'Physical activity', 'description': 'The intervention is administrated through a computerized application as prescribed exercises (cognitive or physical). The specific measures that will be used to determine the effect of the intervention are psychological variables (mood, anxiety, well-being, cognitive variables...) and physical ones (Heart rate variability, stress biomarkers, fat and muscle mass, blood circulation...).', 'armGroupLabels': ['Group 1: physical activity then cognitive training', 'Group 2: Cognitive training then physical activity']}
- {'type': 'BEHAVIORAL', 'name': 'cognitive training', 'description': 'The intervention is administrated through a computerized application as prescribed exercises (cognitive or physical). The specific measures that will be used to determine the effect of the intervention are psychological variables (mood, anxiety, well-being, cognitive variables...) and physical ones (Heart rate variability, stress biomarkers, fat and muscle mass, blood circulation...).', 'armGroupLabels': ['Group 1: physical activity then cognitive training', 'Group 2: Cognitive training then physical activity']}
- {'type': 'BEHAVIORAL', 'name': 'combined physical and cognitive training', 'description': 'The intervention is administrated through a computerized application as prescribed exercises (cognitive or physical). The specific measures that will be used to determine the effect of the intervention are psychological variables (mood, anxiety, well-being, cognitive variables...) and physical ones (Heart rate variability, stress biomarkers, fat and muscle mass, blood circulation...).', 'armGroupLabels': ['Group 3 : resonance frequency breathing then combined physical activity and cognitive training']}

Primary Outcomes:
- {'measure': 'Episodic memory performances', 'description': 'Scores are obtained from delayed memory recall tests from the logical memory subtest of the Wechsler memory scale. It consists of two short narrative stories with an immediate recall phase after each story and a delayed recall phase after 10 minutes. During the delayed recall, each correct detail was awarded with one score point. On a scale of 0 to 50, a higher score means a better detailed recall.', 'timeFrame': 'Month 1 (Between 1 day and a week before and after the first intervention)'}
- {'measure': 'Episodic memory performances', 'description': 'Scores are obtained from delayed memory recall tests from the logical memory subtest of the Wechsler memory scale. It consists of two short narrative stories with an immediate recall phase after each story and a delayed recall phase after 10 minutes. During the delayed recall, each correct detail was awarded with one score point. On a scale of 0 to 50, a higher score means a better detailed recall.', 'timeFrame': 'Month 2 (a week after the second intervention)'}
- {'measure': 'Episodic memory performances', 'description': 'Scores are obtained from delayed memory recall tests from the logical memory subtest of the Wechsler memory scale. It consists of two short narrative stories with an immediate recall phase after each story and a delayed recall phase after 10 minutes. During the delayed recall, each correct detail was awarded with one score point. On a scale of 0 to 50, a higher score means a better detailed recall.', 'timeFrame': 'Month 3'}

Please estimate the sample size based on the assumption: 
Three predictors, significance level of 0.05, statistical power of 0.95, and using the 'pwr' package in R software.
Sample size
        The main objective will be to verify whether the improvements in physiological parameters predict the improvement of different psychological variables. This hypothesis will be tested by performing a multiple linear regression with three physiological variables (score composite of fitness level, HRV and stress biomarkers) as predictors. To conduct a power analysis, data obtained using a physical exercise intervention assessing the association between improved HRV and executive performance was used as a reference.64 The authors reported a correlation of r=.44,pÂ§amp;lt;.05 between cardiac functioning and the number of errors on a battery of cognitive tests. To obtain Cohenâs f2,69 the following formula was applied f2=R21-R2. With R2=.19, a result of f2=.24 was obtained. On the R software,70 power analyses was performed using the âpwrâ package,71 with three predictors, a cut-off at 0.05, and a statistical power of 0.95, revealed a total sample size of 72 participants (24 participants per group). To ensure sufficient statistical power for secondary objectives as well, a total sample size of at least 81 individuals will be targeted (27 individuals per group).