A system model is developed where the criterion to partition the world into a system and a rest is based on the functional relation between its states. This approach implies that the gestalt of systems becomes very dynamic. Especially interactions between systems may create temporary super systems "on the fly". The reference to the function notion establishes the link to computation. Based on the distinction between the intended determinism versus nondeterminism of the interaction, two classes of system interactions are distinguished: composition and cooperation. Composition means that by interaction super systems are created and the interacting systems become subsystems. Cooperation means that systems sensibly interact loosely without creating any identifiable super system function and therefore without super system creation from the perspective of the interacting systems. Cooperative system interactions are described with the help of the protocol notion based on shared states, interpreted as the stateful exchange of characters via Shannon channels between roles - the projection of systems onto the interaction channels. It is shown that roles can be internally coordinated by a set of rules, leading to a very flexible process notion which unfolds its full potential only in a new type of execution environment capable of executing spontaneous transitions. The system model has immediate implications for componentization which can be viewed as an attempt to either hide functional recursion and provide only functionality whose composition behavior is easy to understand, or to provide loosely coupled interactions via protocols. To be complete, component models should therefore at least support three general classes of components: one for loose coupling, one for hierarchical composition, and one for pipes.
In my opinion it is false to conclude from the non-functional relation of the reactive systems to their interaction partners to their somehow non-functional functioning - or ''mode of operation''. Even reactive systems work in a step wise mode and at least for technical systems the simple fact holds that for being constructable, there has to be a function to be implemented - the system function. The main difference between ''transformational'' and ''reactive'' systems in the sense of David Harel and Amir Pnueli is not their functioning but - as they correctly point out - their relation to their environment. For ''transformational'' systems their interfaces towards the interaction provides access to the full system function and thereby provides deterministic interactions. ''transformational'' systems are composed hierarchically by composition according to the definition of sub super systems . By contrast, as I proposed already in @cite_3 , the interfaces of ''reactive'' systems provide access to at least two different projections of the systems, which I call ''roles'' and thereby only provide nondeterministic interactions.
@cite_3
176707287 1546220007 2099640060 2962724035
Our researches on adaptive systems are inspired by their ability of building by themselves a representation of their surrounding world. Using cooperation as a local criterion of self-organization, we study in a network of neuro-agents the evolution of the system and in the same way, the emergence of a functioning coherent with the environmental feed-back. In this paper we expose the abilities of the neuro-agents that give them the autonomy required to build an ab nihilo topology. And finally we want to emphasize the dynamic of the network organization that is basically its best property of adaptation to a changing environment. The work presented here concerns our approach to self-organization in a dynamic neural network. We present some experiments of emergent learning based on our knowledge of complex systems through multi-agent systems technology and cellular biology. In fact we are most interested in the mechanisms involved in the construction of a network able to stabilize its structure in a given environment, than in the efficiency of the learning supported by this structure. Obviously those two ontogenetic processes are strongly coupled and appear simultaneously as mutual consequences. Under those conditions, we conceive artificial systems presenting an inherent complexity close to biological systems as they are open and as their structure evolves from nothing (at least an empty shell) up to an organized, stable and functional network of neuro-agents. Our working hypothesis tells minimal entities of such a system can be built and given with sufficient behavioral potentialities in order to organize themselves to satisfy the whole system activity. In this study, we want to show that a coherent and useful system can emerge without any global model for its functioning, solely from activity and organizational rules of its sub-parts; only agents are designed, not the topology of the network they will belong to. Our thought process supposes four distinct steps that description will be formerly extended. Firstly the neuro-agent unit has to be designed, their properties, their abilities (calculus, communication) and their knowledge. Secondly, initial system is constituted of a minimal number of unlinked neuro-agents. Those pre-built neuro-agents are only receptors (inputs) and actuators (outputs) of the network. Thirdly the global system has to be plunged in a dynamic and open environment in which it will have to adapt to; regarding neuromimetic systems, this phase suppose Some observations are made concerning the process of developing complex systems. A broad class of systems, termed reactive, is singled out as being particularly problematic when it comes to finding satisfactory methods for behavioral description. In this paper we recommend the recently proposed statechart method for this purpose. Moreover, it is observed that most reactive systems cannot be developed in a linear stepwise fashion, but, rather, give rise to a two-dimensional development process, featuring behavioral aspects in the one dimension and implementational ones in the other. Concurrency may occur in both dimensions, as orthogonality of states in the one and as parallelism of subsystems in the other. A preliminary approach to working one’s way through this “magic square” of system development is then presented. The ideas described herein seem to be relevant to a wide variety of application areas. Taking an interaction network oriented perspective in informatics raises the challenge to describe deterministic finite systems which take part in networks of nondeterministic interactions. The traditional approach to describe processes as stepwise executable activities which are not based on the ordinarily nondeterministic interaction shows strong centralization tendencies. As suggested in this article, viewing processes and their interactions as complementary can circumvent these centralization tendencies. The description of both, processes and their interactions is based on the same building blocks, namely finite input output automata (or transducers). Processes are viewed as finite systems that take part in multiple, ordinarily nondeterministic interactions. The interactions between processes are described as protocols. The effects of communication between processes as well as the necessary coordination of different interactions within a processes are both based on the restriction of the transition relation of product automata. The channel based outer coupling represents the causal relation between the output and the input of different systems. The coordination condition based inner coupling represents the causal relation between the input and output of a single system. All steps are illustrated with the example of a network of resource administration processes which is supposed to provide requesting user processes exclusive access to a single resource. We give a detailed description of the geometry of single droplet patterns in a non- local isoperimetric problem. In particular we focus on the sharp interface limit of the Ohta- Kawasaki free energy for diblock copolymers, regarded as a paradigm for those energies modeling physical systems characterized by a competition between short and a long-range interactions. Exploiting fine properties of the regularity theory for minimal surfaces, we extend previous partial results in different directions and give robust tools for the geometric analysis of more complex patterns. where u is the order parameter of a two-phases system confined in ⊂ R n , and and m are two nonnegative numerical parameters. The two terms in the energy mimic attractive short-range and repulsive long-range energies between the phases. More precisely the first term is local, it favors minimal interface area and drives the system toward a partition into few pure phases while the second term, involving a Coulomb-like kernel G, is non-local and favor a fine mixing of the phases. A detailed description of the energy is given in § 1. The competition between these two terms is expected to induce the formation of highly regular mesoscopic patterns, whose geometry strongly depends on the choice of the parameters and m (e.g. spherical spots, cylinders, gyroids and lamellae). 0.1. The Ohta-Kawasaki functional for diblock copolymers. The model we consider arises as a simplification of a Ginzburg-Landau functional proposed by Ohta and Kawasaki in their pioneering paper (41) as a possible description of a diblock copolymers' (DBC) system. Even though it is questionable whether such an energy actually describes DBCs (see Choksi and Ren (15), Muratov (39) and Niethammer and Oshita (40)), nevertheless it is a first, and mathematically non-trivial, attempt to capture some of the main features of these systems. For such a reason it deserved over the last twenty years great attention from both the mathematical and the physical