## 1 Introduction  
Locomotion in mammals, including humans, is largely based on the activity of neural circuits located in the spinal cord (central pattern generators, CPGs) [1, 2]. Although it has been shown that neural networks that determine the pattern of muscle activity and interlimb coordination are located in the spinal cord [3], supraspinal centers are an important and necessary element of locomotion control in mammals. There is evidence that the motor centers of the brain, and, in particular, the motor cortex, play a significant role during walking in humans [4, 5, 6], as well as in rhythmic arm movements associated with stepping [7]. The human spinal cord's lumbosacral and cervical regions are both capable of rhythmogenesis [8]. Depending on the conditions of movement organization, such as when the limbs are unloaded in a horizontal gravity-neutral body position, external, non-invasive influences like muscle vibration [9], tonic electrical stimulation of the peripheral nerves [10], direct electromagnetic stimulation of the spinal circuitry [11], or transcutaneous or epidural electrical stimulation [12; 13; 14] can activate the generators of rhythmic lower and upper limb movements.  
Concerning the motor centers of the brain, transcranial magnetic stimulation (TMS) can be used to study the excitability of motor cortex neurons and their influences on spinal networks [7; 15; 16; 17]. TMS of the motor cortex causes short-latency motor responses (motor-evoked potentials, MEPs) in target muscles mediated by the pyramidal tract [18]. The magnitude of the MEP in the muscle is also affected by its EMG activity at the time of stimulus application. The ratio of the MEP to the background muscle activity is larger during a motor act with a significant amount of motor cortex participation than during actions when the cortex is less involved [19]. The MEPs during non-voluntary locomotor-like leg movements induced by muscle vibration are smaller than the MEPs during voluntary cyclic leg movements, suggesting a lower involvement of the motor cortex in the former case [16]. Concerning the state of the cervical spinal cord, it is less clear whether similar supraspinal impacts vary depending on the type (voluntary or evoked) of rhythmic movements of the upper limbs. It should also be mentioned that the motor cortex may control the arm movements to a greater extent than the lower limbs [20; 21].  
In this study, we examined the effects of TMS of the motor cortex during non-voluntary (vibration-induced) arm oscillations and also compared them with those during voluntary rhythmic arm movements. A number of studies have investigated the effect of arm muscle vibration on corticospinal excitability by examining MEPs in different arm muscles [22; 23; 24; 25; 26], different postures [27], or with partial weight unloading [28], although they have mainly been conducted in the sitting or standing position and did not specifically address the rhythmogenesis of the cervical spinal cord. Rhythmic arm muscle activation is an inherent part of numerous human locomotor activities (walking, running, swimming, cycling, crawling, skiing, etc.), and additional interest in investigating cervical spinal cord activation is due to the fact that it shares spinal control mechanisms with lower limb rhythmogenesis and arm-leg coordination [29; 30; 31], which may also have clinical implications. Therefore, apart from examining MEPs, the impact of supraspinal inputs might be significant when it comes to entraining and activating the spinal CPG networks.