Mathematical models and computation methods for information processing and transmission in neuronal systems subject to stochastic dynamics.

The aim of this project is to harness the research activities of a sizable group of professors and research associates from Naples (Federico II), Salerno and Torino Universities into a co-ordinated effort. In the past, all these people did collaborate to researches closely related to the current theme. Hence, they already possess a mastery of complementary competences in methods of analysis and design of biomathematical models, and in particular of neuronal modeling, both from a theoretical and a computational point of view. The purpose of the present project is to contribute to the development of methods and algorithms suitable for the analysis and simulation of neuronal units that are subject to various types of random perturbations and stimuli. Moreover, the project aims at developing procedures and codes suitable to obtain numerical solutions of the related evolution equations and to assess robustness and stability of the devised models versus random noise and other kinds of random perturbations. Furthermore, we purpose to set up and use of mathematical methods of reliability and renewal theory to describe information in sequences of spike trains. We point out that the proposed research project is well in line with the core of scientific research of the National Coordinator and of the members of the three Units, well focused on the analysis and interpretation of spike-trains modeling sequences of action potentials generated by single neurons especially, but not only, under spontaneous activity conditions. Moreover, in the three Units young members are present, who will contribute to the research developments by opening new investigation pathways. It should also be underlined that, though with individually peculiar interests, the members of the research Units possess diversified expertise. In addition, each group includes some researchers that are particularly well known for their numerical and informatics competence. By making also profit of synergetic and complementary results obtained within the sphere of previously financed programs, we will dwell upon inter-related themes. In short, these consist of designing and extending analytical methods for modeling and mathematically describing neuronal dynamics. The use of the more realistic non Markov models, as well as the search for methods suitable for the description of the dynamics of neuronal networks is a twofold feature of the proposed research. In such a respect, it will be necessary to study the asymptotic behaviors of first-crossing-time densities for Gauss-Markov processes with a view to make use of them for devising efficient numerical procedures and to extend the description of neuronal activity by return process in the presence of refractoriness. Much of the efforts of the participants will be directed to the study of stochastic models for the description of the activity of single neurons based on an integrate-and-fire scheme, with a particular reference to the reach international panorama in this area. The definition and analysis of suitable measures for the description of the information in point processes modeling sequences of neuronal spikes and the development of reliable methods to estimate the parameters of the proposed stochastic models will also be an essential part of the project. The obtained results for single neurons will also be implemented to investigate on the behavior of neuronal networks, which will partly include the design of methods and approaches for the multivariate description of the network. Last, but not least, we foresee the possibility of enrolling young graduates and Master students to work on their dissertations focusing on some of the above-sketched research lines. During its development, the proposed research will benefit of the ongoing collaboration of outstanding colleagues from various international scientific institutions especially in Japan, USA, Spain, France, Czech Republic and Denmark, particularly to the vanguard in the areas of the present project. In conclusion, on the base of the expertise and experience of the participating members, also witnessed by their numerous publications in this area, as well as by the international conferences organized and chaired by the Scientific Coordinator, the development of this program appears to be feasible, original and finalized towards results of international relevance.