The main objective of the Action is to increase the knowledge on the mathematical methods able to estimate the cortical activity and connectivity in the human brain from non invasive neuroelectric and hemodynamic measurements. Additional objectives include the developing of new techniques for the multimodal integration of neuroelectromagnetic and hemodynamic measurements, and their application in several contexts, from the study of human cortical activity during cognitive tasks to the field of the brain computer interface. The NEUROMATH Action aimed to develop an European networks in the neuroscience field which, if possible, should become reference in Europe and contribute to the scientific development of the domain. Scientific research will address questions in the areas listed below. 1. Development of new techniques for the estimation of brain activity and connectivity One of the main objective of this area of research is to increase the knowledge about the accuracy that is possible to obtain for the estimation of brain activity from separate neuroelectric and hemodynamic non invasive recordings. In particular, the possibility is addressed to estimate the cortical activity in selected cortical regions of interest from non invasive scalp EEG recordings. This objective is fundamental since the activity of the brain is generated from the brain and not from the scalp, where it is usually represented. Definitive measure of estimation errors for cortical estimation from non-invasive EEG measurements are to be obtained. Another important goal of this area of research is to increase the knowledge about the estimation of the functional brain connectivity, i.e. how and how much particular regions of the brain cooperate together during cognitive and motor tasks. 2. Multimodal integration of neuroelectric and hemodynamic data. The main objective of this area of research is to understand if the integration of the neuroelectric and hemodynamic measurements improves effectively the estimation of the brain cortical activity and connectivity with respect to the estimation that could be performed using only one separate modality (i.e EEG or fMRI). The benefits are in terms of increased understanding of the physiologic link between hemodynamic and neuroelectric phenomena. 3. Non invasive study of motor and cognitive brain The main objective of this area of research is to understand if the knowledge about basic motor and cognitive processes in humans could be improved by using the advanced mathematical tools developed and tested during this Action, when compared with those already obtainable with standard EEG and fMRI methods. The benefits are in terms of increased understanding of human basic cognition mechanisms. 4. Application of advanced techniques for estimation of brain activity in the brain computer interface area An increased capability to estimate brain activity from non invasive neuroelectric and hemodynamic measurements is opening the way for new scientific research areas. The main objective of this area of research is to increase the knowledge about the use of the brain signals to drive directly external devices, such as virtual keyboards or neuroprosthetic arms without any overt muscle movements. The benefits are in terms of a new class of devices and services driven directly by mental thoughts. 5. Outcomes of the project The implementation of each of these instruments has a considerable impact on the way EEG, and fMRI research is done and organised in Europe. The consulting expertise of the NEUROMATH Action members may help establish a reliable and efficient pan-European bridge between industrial companies and academic institutions. Moreover, a substantial progress in theoretical and applied research is expected from the direct collaboration between most of the partners from several disciplines and the European industries in the field of neuroelectric and hemodynamic measurement devices.