Applied Mathematics

Responsabile scientifico/Coordinatore
RINALDI Maurizio

Attività e competenze

Mathematical modeling and statistical learning
·       GEOMETRY 3D COMPLEX STRUCTURES. POLYMERS AND PROTEINS Proteins are an intriguing example of 3D structures consisting of a large number of points with connections, but many other interesting objects can be found. The study of their geometry and topological properties can be implemented also by using computer algebra systems. In particular beside graphical representations one could implement algorithms to compute topological invariants (e.g. link polynomials) and geometric invariants.
·       DATA MINING, MULTIVARIATE DATA ANALYSIS, CLUSTER ANALYSIS AND PATTERN RECOGNITION We use a variety of different data mining and multivariate data analysis techniques, particularly a wide range of cluster analysis and pattern recognition methods, which include: principal component analysis, neural networks of various kinds (both supervised and unsupervised), and a wide range of classification algorithms. The further use of genetic algorithms makes it possible to optimize the technique at hand. These techniques can be applied to a wide range of data in particular to data of biological, medical or pharmaceutical origin.
·       MATHEMATICAL MODELS AND SIMULATION OF COMPLEX PHENOMENA Life sciences traditionally offer a wide range of problems whose solutions escape traditional methods. In many biological situations, for instance the construction of ad hoc dynamical models allows a better understanding, and can lead to quite interesting results. The models could result in systems of complex equations (e.g. non linear difference equation) and the search for their solutions requires the development of new mathematical skills. A wide use of emerging numerical techniques is often extremely helpful to find good approximations of the solutions. Also computer simulation models of complex phenomena allow very often to gain some insight and to deepen understanding and forecasting ability.
·       HIGH THROUGHPUT DATA ANALYSIS Microarray is a multiplex technology used in molecular biology and medicine in order to measure differential gene expression or microRNA profiling. Statistics play a fundamental role in experiment design and gene expression profile, which requires handling of large amount of data. This is just one example of a high-throughput technique that deserve a particular treatment of data.
Software expertise (Mathematica and R)

Settore ERC del gruppo
PE1, LS2