## 4 Discussion
More recently, the traditional NMF algorithm was extended to produce Mixed Matrix Factorization (MMF), a novel factorization method that incorporates any kind of unconstrained variable into the factorization ([PERSON] et al., 2018). The method was conceived to mathematically support the new notion of \"kinematic-muscular synergies\", that needed to allow the factorization of variables that could either be positive (when a joint is flexed) or negative (when a joint is extended). Kinematic-muscular synergies provide a biomechanically oriented characterization of motor control as they incorporate both the muscular activation and the functional joint output ([PERSON] et al., 2019). Another attempt comes from the work of [PERSON] group ([PERSON], 2019), who use information theory to describe how multichannel EMG relates to task space variables. Incorporating task space variables might result in a major step toward the applicability of muscle synergies to sport, as each neural activation would be linked directly to the motor outcomes they produce, providing a versatile tool potentially applicable to performance optimization, understanding of risks of injury, rehabilitation, and more. This approach is potentially useful for the analysis of all sports because it allows us to explain better how the neutrally originated synergy weights are linked with motor task performance. In particular, this method could be useful to study movements in sports where it is not easy to assess the biomechanical function of synergies through muscle activation analysis alone. Typical examples may be movements not cyclic in nature, composed of many phases. Some examples might be the high and long jump or the spike gesture in volleyball. Indeed, these sports involve gestures that require complex sequences of movement and/or aggregated multi-task motion, which may largely benefit from task-related synergistic approaches. For example, to perform a high-performance long jump, it is first needed to prepare a good run-up. Therefore, it is important to know which muscles are involved during the run-up, separating them from those involved during the jump deadlift in order to understand which muscle activations are necessary for each gesture phase to achieve an optimal jump performance. Incorporating task variables into synergies would help to segment and quantify properly more complex gestures and could be useful to identify how coaches could train the muscles responsible for the run-up in order to improve muscle activation during the jump and make it more effective. The same concepts can be applied in the volleyball spike because the power and the efficacy of a spike are affected by the correct execution of the three steps before jumping. Adding kinematic and biomechanical information to the synergy composition would make EMG measurements more related to joint motion, paving the way for an increased understanding of sports gestures. Figure 1 shows an example of kinematic-muscular synergies and their corresponding temporal coefficients during human locomotion. This figure is an original representation and it has been created using data from the gait study by [PERSON] et al., in which a gait analysis on a subject who performed four steps was executed ([PERSON] et al., 2019); the EMG was estimated with a biomechanical simulation and its envelope was used as input for the MMF algorithm in order to extract the spatial kinematic-muscular synergies ([PERSON] et al., 2019). In these synergies, both the muscle activations and the joint activities were highlighted. W1  
shows the activity of the psoas, adductor, gastrocnemius, and soleus associated with ankle plantar flexion and the flexion of the knee and hip and activates at the end of the stance phase during the propulsion. W2 shows the glutei, biceps femoris, and rectus femoris activated at the beginning and the end of the gait cycle for flexing the knee and hip. W3 is predominantly muscular with the semitendinosus, semimembranosus, vastus medialis, and lateralis activated during the stance phase.