The idea of existence of a mechanism that governs the formation of forms of auto- organization into dynamic equilibrium systems is to base of the study of complexity.Complex systems are constituted by simple, independent, interactive, adaptive and evolutionary elements that develop a form of auto- organization that allows to the system to acquire evolutionary emergent complex properties. Molecule, embryo, nervous system, immune system, ecosystem, economy, culture and religion are examples of such systems. The creation of evolutionary adaptive biological system forms of order of increasing complex levels is favoured by a tendency opposed to the entropy, that is the degree measure of casualness and disorder of a system.In a system the passage from a level to an other more complex is defined phase transition. In first order phase transition this passage is abrupt, while in second order phase transition the system dynamically mixes order and chaos, finding a dynamic equilibrium in the transition point defined edge of chaos. In the edge of chaos the system stops being predictable but it’ s not chaotic. A chaotic system (as atmospheric phenomenon) presents characteristics of strong unpredictability, extreme sensibility to initial conditions and scale variations. Complex systems remain at the edge of chaos in the second order phase transition also for the capability to memorize, elaborate and transmit information (computational capability). The adaptation, that induces emergent entities to increasing complex levels, derives from selection and mutation in reproduction processes in biological systems or from learning and experience in social systems. In the co-evolution elements of system adapt themselves one to others evolving toward more functional forms to the environment in which they operate. More systems can interact, forming superior level systems. An issue for artificial life is the study of the emergence of complex properties. In artificial life systems the elements interact at local level without a central control, evolving in complex phenomena, as in nature. Cellular automata are an example of very complex configurations with characteristics of auto-organization and emergency, evolving from a simple mechanism of interaction and a series of parameters, genetic algorithms simulate evolutionary biological mechanisms, artificial neural nets use parallel elaboration of information. The agents in an artificial life system can reproduce themselves, they evolve and interact into the system and with environment adopting strategy of co-operation and competition. These few examples demonstrate that the complexity, product of a particular organization of the system, can be find also in a “life” different from natural one. The Evolutionary System Group has investigated this research area

The label Psychology of Programming has been adopted to indicate a research area that investigates "the psychological aspects of programming and the computational aspects of psychology", where 'programming' signifies all the meanings including the process of software development . In particular, the psychological issues that pertain to programming, the theoretical and methodological issues of design, skill acquisition, expert programming and other fundamental problems are investigated. The main topics (drawn on the 10th annual Workshop of the Psychology of Programming Interest Group, PPIG) are: 

• programming tasks (e.g. comprehension, creation, documentation, modification, debugging, testing);
• reasoning and planning (e.g. strategies, programming plans, formal reasoning, display-based reasoning);
• cognitive models;
• programming notations and representations; 
• programming paradigms;
• learning programming;
• software engineering (e.g. programming in the large, re-use, maintenance, scale, specification);
• social and organisational issues;
• collaboration (including CSCW);
• programming tools (e.g. environments, CASE, editors, navigation tools);
• differences among programmers.

Psychology of Programming is a multidisciplinary sector whose components attempt to address the topics I mentioned before from different perspectives, these disciplines will be presented to ascertain what is pertinent to Psychology of Programming (Bilotta, 1998).

Evolutionary robotics is a new technique for the automatic creation of autonomous robots. It is inspired by the darwinian principle of selective reproduction of the fittest. It is a new approach which looks at robot as autonomous artificial organism that develop their own skills in close interaction with the environment without human intervention. Hevily drawing from natural sciences like biology and ethology, evolutionary robotics makes use of tools like neural networks, genetic algorithms, dynamic systems and biomorphic engineering. The term evolutionary robotics has been introduced only quite recently (Cliff, Harvey and Husband, 1993), but the idea of representing the control system of a robot as an artificial chromosome subject to the laws of genetics and of natural selection dates back to the end of the 1980's when the first simulated artificial organisms with a sensory motor sistem began evolving on computer screens. In the very last few years evolutionary robotics has gathered the interest of a large community of researchers with different research interests and background (ranging from AI and robotics, to biology and cognitive sciences, to the study of social behaviour). At present, the main research performed in the group regards the biological and evolutive aspects of complex behavior in order to understand the relations between a simple sensory-motor reaction, showed from the insects to the humans, respect of more complex behavior, i.e. learning and planning, which involves cognitive structure of high-level order, such as memory, which strongly seems to determine the most part of cognitive difference between natural organisms. In addition, some explorations in the field of body-brain co-evolution has been done.

Educational Technology is a sector of research, which is interested in creating tools for improving learning possibility, augmenting  the student's capabilities, in the cognitive domain . In this context, many softwares have been realized which give the possibility to represent and simulate complex phenomena and to analyse them improving abilities and competencies.We should like to realize what is called "Educational Robotics" (Martin, 1990), the sector which offers the possibility to simulate cognitive functions, in order to compare the system built performances with the system or the theory or the cognitive functions in designing physical robots that wants understand.Lego MindStorms is an educational kit that gives children the possibility to play with mechanical robots, to programme them and to make them behave in a real world situation (…). Learning to programme robot’s control means children acquiring some specific competence (Bilotta, Pantano, 2000). Fred Martin (1990) underlines that using these captivating technologies, it is possible to notice as, many students, which are not insert very well in the learning context, acquire a new sense of their intelligence and their innate ability.The future of the educational technologies is to engage really children’s minds, to simulate their creativeness and to prepare them for the future. The future also consists of using the computer as a tool of communication and to access at the global information (Cypher, 2001)

Solving real world problems and developing contacts with industry are the main aims of industrial mathematics. In this field the research activities of our group are concerned with:

• The description of charge transport in semiconductors and eletronic device simulation.
• Tolerance Analysis, Uncertain Modeling, Fuzzy System
• Non Linear Propagation, Reduction Methods
• Non-linear phenomena and complexity theory
• Man-computer interaction and new technologies.

Enhanced functional integration requires an increaseangly accurate modeling of charge transport in semiconductors. The standard drift diffusion models cannot cope with high field phenomena since they do not comprise energy as a dynamical variable.Therefore new models, loosely named hydrodynamical models, have been constructed in order to describe phenomena such as hot electron propagation, impact ionization and heat generation in electronic devices. These hydrodynamical models are derived from the infinite hierarchy of the moment equations of the Boltzmann transport equation by suitable truncation procedures.A theoretically founded method of obtaining the closure of the balance equations is based on the theory of extended thermodynamics and it exploits the maximum entropy method.  These hydrodynamical models have been used to describe the electric properties of bulk Si and GaAs semiconductors, both in the parabolic  and in the Kane approximaton for the electron dispersion relation.
Applications to electronic devices, with particular attention to n⁺-n-n⁺ ballistic diodes and Gunn diode, and comparisons with Monte Carlo results have shown the validity of these new models. The numerical solutions have been obtained by means of Nessyahu-Tadmor central schemes. Tolerance analysis is a very important design tool for industrial processes. The usual method for tolerance analysis is Monte Carlo simulation, which, however, is extremely CPU intensive, since it needs to generate a large sample of function values in order to yield statistically significant results. Recently new methods have been introduced in several fields, which for some classes of problems might be a viable alternative to Monte Carlo simulation.

Uncertainty is a general term that encompasses imprecision, incompleteness, vagueness, ambiguity, etc. In applied mathematical problems uncertainty is introduced in many ways, e.g :

• uncertainty as a result of imprecise measurements. This is a rather usual form of uncertainty, which may be described in different
  ways, including a probabilistic setting if sufficient information is provided
• uncertainty due to summarization in the attribute information as when smoothing noisy data in order to construct a sensible
  mathematical representation of the data
• uncertainty arising as vagueness or ambiguity occurring in the definition of systems.

For uncertainty due to imprecise measurements the probabilistic description is found to be sufficiently appropriate if enough data are available. In the other cases the probabilistic approach can be applied only by stretching its meaning and making (sometimes unwarranted) assumptions on the joint probability density function. In situations where a conservative estimate is of interest, i.e. an estimated which would hold under very general premises and does not require very specific assumptions which are rather difficult to check in practice, as in risk analysis, other approaches, such as those based on interval analysis or fuzzy arithmetic could be more appropriate because they do not require very detailed assumption about the data structure.

The idea of existence of mechanism govern the formation of forms of auto-organization into dynamic equilibrium systems is at the base of the study of Complexity.Complex systems are constituted by simple, independent, interactive, adaptive and evolutionary elements that develop a form of auto- organization that allows to the system to acquire evolutionary emergent complex properties