## Theories and Algorithms

Theories and algorithms of artificial intelligence, machine learning and mathematical foundations.

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The theory of complex systems (also known as complexity theory or complexity perspective) arises in part from general systems theory (von Bertalanffy 1968; Warren et al. 1998). It focuses on understanding complex systems or complex adaptive systems. Complex systems often encompass a (often large) number of entities and subsystems, of which there are often multiple interactions, non-linear relationships, feedbacks, thresholds, lags, and adaptations. As a consequence, these characteristics in complex systems can lead to emerging phenomena or to results which are not analyzable only from the components of the system and their attributes.

Modeling of complex systems is defined by the application of various mathematical, statistical and computational techniques, to generate insight into the functioning of some of the most complex physical and natural systems in the world.

Complex systems are those whose properties result from the non-linear interaction of components, such as cells in a body, neurons in a brain, or individuals in a group. Our technical approaches span the gamut from very simple deterministic and stochastic mathematical approximations, from principle-based approaches to dealing with uncertainty, to complex computer and physical simulation in software and robotic hardware. Given their ubiquity, it is difficult to overestimate the benefits of a better understanding of complex systems and the appropriate tools to analyze them.

Understanding and managing complex systems has become one of the greatest challenges for research, policy and industry. The modeling and simulation of complex systems promise to allow us to understand how a human nervous system and brain not only maintain the activities of a metabolism, but also enable the production of intelligent behaviors, how huge ecosystems adapt to changes, or what actually influences climate change.

In addition, artificial systems are becoming more and more complex and difficult, if not impossible to understand. Therefore, we need methods and tools that can help us, for example, to estimate how different infrastructure investments will affect the transport system and to understand the behavior of large internet-based systems in different situations. This type of system becomes the center of research and sustainable management because there are now techniques, tools and IT resources available.