Franciszek Grabowski

Nonextensive model of self-organizing systems

The article concerns the new nonextensive model of self-organizing systems and consists of two interrelated parts. The first one presents a new nonextensive model of interaction between elements of systems. The second one concerns the relationship between microscopic and macroscopic processes in complex systems. It is shown that nonextensivity and self-organization of systems is a result of mismatch between its elements.

TOWARDS POSSIBLE NON-EXTENSIVE THERMODYNAMICS OF ALGORITHMIC PROCESSING — STATISTICAL MECHANICS OF INSERTION SORT ALGORITHM

Tsallis entropy introduced in 1988 is considered to have obtained new possibilities to construct generalized thermodynamical basis for statistical physics expanding classical Boltzmann–Gibbs thermodynamics for nonequilibrium states. During the last two decades this q-generalized theory has been successfully applied to considerable amount of physically interesting complex phenomena. The authors would like to present a new view on the problem of algorithms computational complexity analysis by the example of the possible thermodynamical basis of the sorting process and its dynamical behavior. A classical approach to the analysis of the amount of resources needed for algorithmic computation is based on the assumption that the contact between the algorithm and the input data stream is a simple system, because only the worst-case time complexity is considered to minimize the dependency on specific instances. Meanwhile the article shows that this process can be governed by long-range dependencies with thermodynamical basis expressed by the specific shapes of probability distributions. The classical approach does not allow to describe all properties of processes (especially the dynamical behavior of algorithms) that can appear during the computer algorithmic processing even if one takes into account the average case analysis in computational complexity. The importance of this problem is still neglected especially if one realizes two important things. The first one: nowadays computer systems work also in an interactive mode and for better understanding of its possible behavior one needs a proper thermodynamical basis. The second one: computers from mathematical point of view are Turing machines but in reality they have physical implementations that need energy for processing and the problem of entropy production appears. That is why the thermodynamical analysis of the possible behavior of the simple insertion sort algorithm will be given here.

Simple, complicated and complex systems — the brief introduction

Systems are very popular, in the world that we live. On the one hand they can be as small as atoms, on the other hand they can be compared to the whole universe, which is a huge system in itself. The first systems were, of course, those natural ones - the nature created them; nowadays there are also manmade systems. Despite the fact that man has observed them both for ages, not long ago was it realized that they have got, in many cases, the same structures independently on system type, are governed according to the same laws and the processes existing inside them can be simulated by interdisciplinary models. The main goal of this article is to present the basic notions connected with complex systems and the conception of the system approach.

Wireless Networks Environment and Complex Networks

Models describing the wireless network environment in most cases are based on the assumption that they are simple systems. However, the parameters describing this type of networks are particularly sensitive to the volatility of the operating conditions. Simple systems take only two operating states into account apart from an overload state, i.e. underload state and a state of equilibrium at the limit of the system. However, the overload state is normal and acceptable by actual natural systems. Wireless networks often operate on the border of a balance between available resources and expectations for the implementation of communication tasks. Therefore, the paper will introduce wireless network especially WLAN in terms of complex systems moving away from the current reductionist paradigm. In addition, there will be presented the method of the dynamic allocation of resources (bandwidth) that is based on properties of complex systems.

Long-range dependencies in algorithmic computing

An article shows the problem of existence the long-range dependencies in algorithmic computing. A brilliant idea of Turing machine, which is the basis of all theoretical considerations in the contemporary computer engineering, seems to be, from the system analysis point of view, only a complicated system that works only under an algorithmic processing mode. Meanwhile, taking into account the physical structure, the character of realized tasks and the interactive processing mode of nowadays computer systems, one may concluded that they are complex systems, whose analysis requires a definitely different approach. It will be achievable when the widest possible context, which requires: the complex systems approach, the proper thermodynamical analysis and the knowledge about the idea of paradigms changes will be taken. In the case of computer science, where the paradigm of algorithmic computing is changed towards interactive computing the problem of existence long-range dependencies is crucial because such a property degrade the performance of computer systems. The ancient rule divide and conquer (reductionist approach) canpsilat be used in the case of complex systems, because they are governed by Aristotle rule the whole is more that sum of its parts. Thus the analysis of modern computer systems requires the understanding of general laws that govern it as a whole and also a different, system approach that takes into account the long-range dependencies in time and space domain.