Consecutive PSP patients were recruited and underwent a review of the medical history, a neurological examination including the PSP rating scale (PSPRS)  and a comprehensive cognitive and behavioural assessment . Inclusion criteria were (1) clinical diagnosis of probable PSP according to current criteria , (2) the ability to stand alone without support and (3) the ability to walk at least 3 m without aid. Exclusion criteria were (1) dementia, (2) vestibular/proprioceptive or sensory abnormalities and (3) any contraindication to perform brain stimulation.
All subjects gave written informed consent prior to participation. The local ethics committee approved the study (protocol 193/16), recorded as NCT04222218 in clinicaltrial.gov. The study was performed in accordance with the Declaration of Helsinki.
Repetitive Transcranial Magnetic Stimulation
Each patient received both rTMS and sham cerebellar single-session stimulations in randomised order in two different sessions performed at the same time of the day, separated by at least 2 weeks. The patient and the examiner were blind to the type of rTMS delivered, applied by another experimenter. Repetitive cerebellar theta burst stimulation was performed by Duo-Mag XT100 (Deymed -Horonov, Czech Republic) according to the protocol described by Brusa and coauthors . The coil was placed tangentially to the skull over the lateral cerebellum 1 cm inferior and 3 cm right to the inion. Three 50-Hz pulses were repeated at a rate of 5 Hz; 20 trains of 10 bursts with 8-s intervals for a total of 600 pulses and for total time of 240 seconds were applied . The intensity of rTMS was set at the 80% of the resting motor threshold obtained in the left motor cortex for each subject. For sham simulation, a spacer was attached to the coil; the stimulation parameters, the coil position and the sound were identical to the active condition.
Dynamic Mobility and Mobile Health Technology-Instrumented Static Balance Assessment
All subjects underwent a clinical evaluation including the Tinetti test, the Short Physical Performance Battery (SPPB), the Timed Up and Go test and the Functional Reach test (FR) before and after stimulation . Static balance was tested before and after each stimulation with four tasks of 30-s duration, respectively: tandem and semitandem stance with eyes closed and with eyes open (Supplementary Figure 1). Primary endpoint was changes in the time in this position without support. For mobile health technology secondary outcomes, an inertial sensor unit (IMU) with 100 Hz sampling frequency (Rehagait®, Hasomed GmbH, Magdeburg, Germany) was fixed at the level of the third lumbar spine segment close to the centre of mass . Acceleration signals were processed and calculated as previously described . The following sway parameters were extracted: area, mean velocity, mean acceleration (root mean square - RMS), jerk (indicating smoothness of compensatory movements) and mean frequency . Mean velocity, RMS and jerk were calculated for both anteroposterior (AP) and medio-lateral (ML) directions.
Differences in baseline performances between real and sham trials were evaluated using Mann-Whitney test. A two-way repeated-measures analysis of variance (ANOVA) was run to determine the effect of the different treatments over time on assessment, adjusted for baseline values and the sequence of stimulation (real-sham vs sham-real). Significance was set to p=0.05, and SPSS software (version 21; SPSS, Inc., Chicago, IL) was used.