| A Kinematic Theory was proposed a few years ago to analyze rapid human movements. The theory is based on a delta-lognormal equation which can be used to globally describe the basic properties of velocity profiles using seven parameters. This realistic model has been of great use to solve pattern recognition problems (signature verification, handwriting analysis and synthesize, etc.). This model has been demonstrated to successfully fit the experimental data of velocity profiles with a minimum reconstruction error in comparison to twenty six other models dealing with motor control. Afterward, the formal mathematical proof of the convergence was published in 2003. However, this theory is only in its startup applications, and there are several aspects which remain to be developed. For example, it has been showed that it is important to made up a robust extractor of delta-lognormal parameters to deal with experimental data. Furthermore, the proportionality relationship hypothesis of the Kinematic Theory was not yet observed in the behaviors of the neuromuscular system.;From the refutability point of view, the hypotheses of any theory must be subjected to experience, and in many applications, it needs hardware and software tools to analyze real data. Furthermore, one theory is more viable when it escapes the experimental refutability and when it describes one physical phenomenon with simple analytical equations. Besides its descriptive behavior capabilities, any theory should have the ability to predict some behaviors that have not been observed yet. Also, one of the best ways to deduct the strongest importance of any model in relation to other ones dealing in the same domain of application is to compare their concepts and search which concepts are the approximation of others.;In case of the Kinematic Theory, the aims of this thesis are to give some answers to these theoretical requirements. Its main chapters contain the following points: (1) Construction and characterization of a delta-lognormal extractor system, (2) Comparison of the delta-lognormal model with some kinematic model, offering an analytical expression of the velocity profile, (3) Design of a non refutability experience using the surface electromyography signals, (4) Generalization of the Kinematic Theory by proposing sigma-lognormal model, (5) Analysis and synthesis of the handwriting stroke variability.;This research is concluded by describing a new perspective of the theory. It deals with neuroscience and proposes the use of a delta-lognormal equation as a representation of an action potential. Once confirmed by fitting experimental data, it is expected that this new prediction of the Kinematic Theory would certainly open new insights in neuroscience research, by using a delta-lognormal model as an analysis and synthesis instrument dealing with neurophysiologal phenomena.;This thesis was led in the same spirit in which had already developed previous works at the Scribens laboratory. These consist in promoting the Kinematic Theory and proposing new insights. The aims of the present thesis consist in giving some answers to questions raised by the scientific community and in suggesting other applications that have not been investigated by the theory yet. The major contributions of this search begins by proposing another formal mathematical proof of convergence of the impulse response of neuromuscular system toward a lognormal function. This leads to an analytical expression of the error of convergence. Furthermore, the proportionality hypothesis leads to one theorem that underlines the autosimilar infinite divisibility property of a lognormal function. |
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