Spatial structures are fundamental to all areas of biology and ecology. "Spatial structures" are those biological and ecological entities whose functions depend on the spatial relationship of their components. Examples in biology include morphogenesis, pattern formation, angiogenesis, tumor growth, chemotaxis, cytoskeletal mechanics, rabies propagation, seasonal bird migrations, patchy structure of plancton and fish popuations. Spatially distributed processes can be modelled at different scales, depending on the features of interest and on the level of aggregation of their components. Scaling is associated with the choice of representation: from discrete to continuous, from stochastic to deterministic, from ordinary to partial to stochastic differential equations, from cellular automata to particle systems, from mean-fields to individual-based models. With this last approach virtual worlds are created "in silico", mimicking the real world and made up of thousands of individuals, each explicitly represented with its physiology, its social habits.
Its survival and reproductive goals. The behavior of the simulated electronic life forms is then analyzed and compared with known characteristics of biological species. While the field of biomathematics is growing fast in number of applications and range of subjects, spurred by the social impact of biological issues (medical and ecological foremost) and by the availability of cheaper and cheaper computing power, it is generally recognised that the academic opportunities for interdiscipinary instruction are limited, and that the productivity of biomathematical research would greatly benefit if biologists and mathematicians were conversant in and aware of each other's problems. Further, growing specialization makes it necessary for individual researchers to refer to a geographically dispersed scientific community as their common interest group, as single Universities cannot possibly provide the range of competences of which any one field is rich. This summer school addresses the problem of biomathematical interdisciplinary training.