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Many systems in the natural sciences and humanities fall under the heading of "Complex Systems". Many are multi-agent systems, the agents being complex molecules, cells, living organisms, animal groups, human societies, industrial firms or competing technologies.

But what is a complex system?

As always, notions originate from the observation of facts. And the most general observation here is that, when a set of evolving agents interacts, the resulting global system displays collective properties which look qualitatively different from a simple superposition of their elementary behaviors. The common structural features of such systems are non-linearity, interdependence and emergence.

Non-linearity means that the dynamical behavior of the system cannot be viewed as a superposition of the elementary effects of its components, nor reconstructed from elementary "modes". In simple terms, doubling the input does not necessarily double the output.

Interdependence means that the response of each one of the agents, from which the system is built, depends on the evolution of the others, in fact in a self-consistent manner.

Emergence means the creation of collective properties qualitatively different from the individual behavior.

Because these systems share some common structural properties, it is tempting to ask:

Is there a unified theory of complex systems?

Probably not. Unifying ideas like the "the edge of chaos", self-organized criticality, etc, have, at times, been proposed as general paradigms for all complex adaptive systems. But in all cases examples are found of systems that do not follow these general schemes and nevertheless look fairly complex to an unbiased eye. And even if all complex systems arose from the same basic principles, the principles themselves might be of limited utility. (The notion of forest may be useful to understand plant epidemics but is of limited utility to treat a specific tree disease). Complex systems have their specific properties that deserve specialized scientific effort, and for such different corpora different strategies need to be used in order to advance the operative knowledge in each particular field. For complex systems, to learn from their differences is an even more exciting challenge than to find a grand unified theory.

To reach a better understanding of each field and to transfer techniques and insights from one discipline to the others requires the development of a common language and an open forum engaging a broad community to perform a strong cross-fertilization of research. This is why, in this project, mathematicians, physicists, biologists, medical doctors, economists, sociologists, linguists and engineers have attempted to share their experiences, models and the many questions on what role the notion of complexity may play in their fields.

By joint collaborative research and the participation in the seminars and workshops, phenomena and paradigms of fields other than their own became familiar to the scientists that shared the experiences of this project. Simple is what becomes familiar and, by broadening their knowledge on how complexity unfolds in its many forms, they might be able, in the future, to approach the study of complexity through simplicity.


One of the principal objects of theoretical
research in any department of knowledge is to
find the point of view from which the subject
appears in its greatest simplicity.
J. W. Gibbs

Hot spikes

After several preparatory symposia, starting in the April 1998 Madeira Workshop, the Conference "The Sciences of Complexity", held at ZiF, October 6-12, 2000, marked the opening of the Research Year (October 2000 - August 2001). Rather than focus on a particular field it was decided, in conformity with the spirit of the project, to bring together participants from a large spectrum of THE SCIENCES of (with?) complexity. The reader may have a look at this link of the conference, to obtain an insight on how this claim was achieved.

There were special moments when the concentration of participants with specific expertise steered the main stream of the project.

Dynamical models with learning capabilities, for drives and industrial control systems, was at the center of the program during October and November around a group of engineers.

During February a group of experimental physicists carried out, at ZiF, an experiment on shear flow of liquid crystals. This situation, where we can see the coexistence of turbulent and laminar domains, nowadays denoted "space-time intermittency", was at the center of an effort of both experimentalists and theoreticians for a deeper understanding of control and synchronization in extended systems.

Following a first Symposium in October 2000 the dynamics of the immune system was central in March. Here biologists together with computer scientists and physicists focused their interaction on the interplay of cellular and humoral immune systems during the response to viruses, on modeling of vaccination and the isotypic shift.

After a Symposium in July 2000, around May 2001 much attention was paid to the economic development of regions and countries by economists involved on regional and national innovation systems and on mastering complexity in the environment. Information flows may be the central notion to follow, when modeling such systems.

In June, the ability of neural networks (large assemblies of interacting non-linear units) to adapt and perform artificial learning in complex tasks was the topic. Here mathematicians, physicists and engineers collaborated in exploring new supervised and unsupervised learning techniques.

Following a Workshop in February 2000, and always in collaboration with the Tycho Brahe Project, linguists assembled in July 2001. Here two important and long-standing linguistic questions were addressed: how does language change proceed in time, and what triggers syntactic change. Continuing the well established tradition of the Tycho Brahe Project, linguists worked closely with mathematicians, physicists and computer scientists. Such collaboration of the disciplines was one of the hallmarks of the ZiF complexity project.

The newly emerging school of economics called "evolutionary economics" challenges most mainstream approaches in the field by insisting that most, if not all economic phenomena have to be viewed as non-linear out-of-equilibrium dynamics. The working group on economics and learning systems addressed these questions.

In June-July and also at several times during the year probabilistic theories of neural representation, neural networks with higher-order interactions and quantum control were focal points of research at ZiF.

In July and August computational non-linear dynamics and extended systems close to threshold were actively pursued.

To study the dynamics of the evolution at molecular resolution, one must master complexity with incomplete information. The subject was a continually progressing hot spike.

The notion of Self-Organized Criticality has become a new paradigm when studying different phenonema in natural and social sciences. Active research in this area took place throughout the whole year.

Finally, a special week on "Mathematics and Finance" highlighted the lively interactions between these two fields.

This is not the moment to draw final conclusions. The field is wide open and demands a continued and interdisciplinary effort for which the research year at ZiF has been a valuable stepping stone. So, no final conclusions yet, but and opening of windows. To this effort the present CD-ROM should contribute.

The study of complexity in its many forms and the role it plays in science and society is an evolving process. Future working sessions and special research months are planned for the near future. For more information you may contact:

Philippe Blanchard
Josef Fröhlich
Ricardo Lima
Ludwig Streit
Luis Vázquez
Rui Vilela Mendes

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