arXiv subjects

Andrzej Gecow

Publications and source records attributed to Andrzej Gecow.

5 recordsLinked to original sources

arXiv2022

Life is not on the edge of chaos but in a half-chaos of not fully random systems. Definition and simulations of the half-chaos in complex networks

The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a living, technological or social than fully random Kauffman networks. This makes a large change of widely taken view in the dynamics of complex networks. Current theory predicts that random autonomous systems can be either ordered or chaotic with fast phase transition between them. However, modeled adapted systems are not fully random, they are usually stable, but the estimated parameters are usually "chaotic", they place the fully random networks in the chaotic regime, far from the narrow phase transition. It is showed that among the not fully random systems with "chaotic parameters", a large third state called half-chaos exists, which simultaneously exhibit small (ordered) and large (chaotic) reactions for small disturbances in similar share. The discovery of half-chaos frees modeling of adapted systems from sharp restrictions; it allows to use "chaotic parameters" and get a nearly stable system more similar to modeled one. It gives a base for identity criterion of an evolving object, simplifies the definition of basic Darwinian mechanism and changes "life on the edge of chaos" to "life evolves in the half-chaos of not fully random systems".

nlin.AO↗

arXiv2011

The differences between natural and artificial life. Towards a definition of life

It is high time to openly and without finalism define the dangerous but needed term 'purposeful information', whose quantity is an Eigen information value. Using the term 'biological information' in its stead forces one into an uncomfortable detour. I propose such a definition based on the generalized notions of 'information' and 'encoding'. Next, the properties of the spontaneous process of collecting purposeful information are investigated. In effect, the properties of this process: the goal 'continuation of existence', reproduction and Darwinian mechanism are derived which suggest, that it is the natural life process. A 'natural identity criterion' appears in this process for an evolving object, that is connected to a 'small change tendency'. Likewise, 'hereditary information' is defined. Artificial life is constructed by living objects, is a part of natural life process and its properties are not an effect of its internal restrictions but of external assumptions.

nlin.AO↗

arXiv2010

More than two equally probable variants of signal in Kauffman networks as an important overlooked case, negative feedbacks allow life in chaos

There are three main aims of this paper. 1- I explain reasons why I await life to lie significantly deeper in chaos than Kauffman approach does, however still in boundary area near `the edge of chaos and order'. The role of negative feedbacks in stability of living objects is main of those reasons. In Kauffman's approach regulation using negative feedbacks is not considered sufficiently, e.g. in gene regulatory model based on Boolean networks, which indicates therefore not proper source of stability. Large damage avalanche is available only in chaotic phase. It models death in all living objects necessary for Darwinian elimination. It is the first step of my approach leading to structural tendencies which are effects of adaptive evolution of dynamic complex (maturely chaotic) networks. 2- Introduction of s>=2 equally probable variants of signal (state of node in Kauffman network) as interpretively based new statistical mechanism (RSN) instead of the bias p - probability of one of signal variants used in RBN family and RNS. It is also different than RWN model. For this mechanism which can be treated as very frequent, ordered phase occurs only in exceptional cases but for this approach the chaotic phase is investigated. Annealed approximation expectations and simulations of damage spreading for different network types (similar to CRBN, FSRBN and EFRBN but with s>=2) are described. Degree of order in chaotic phase in dependency of network parameters and type is discussed. By using such order life evolve. 3- A simplified algorithm called `reversed-annealed' for statistical simulation of damage spreading is described. It is used for simulations presented in this and next papers describing my approach.

cond-mat.dis-nn↗

arXiv2010

Complexity Threshold for Functioning Directed Networks in Damage Size Distribution

A certain complexity threshold is proposed which defines the term `complex network' for RSN, e.g. Kauffman networks with s>=2 - more than two equally probable state variants. Such Kauffman networks are no longer Boolean networks. RSN are different than RWN and RNS. This article is the second one of three steps in description of `structural tendencies' which are an effect of adaptive evolution of complex RSN. This complexity threshold is based on the appearances of chaotic features of a network during its random growth and disappearance of small network effects. Distribution of damage size (after small disturbance) measured in a fraction of damaged nodes, or in number of damaged external outputs and degree of chaos is investigated using simulation. It is done during growth (up to N=4000 nodes) for different: network types (including scale-free), numbers of node inputs (K=2,3,4, fixed for a network) and numbers of signal variants (s=2,3,4,16). In this distribution two peaks emerge and in-between them there appears an area of zero frequency - this is the best practical criterion of complexity threshold found in the investigation. No critical points are found in the area of emerging complexity. A special simplified algorithm (`reversed-annealed') is used which omits the problem of circular attractors. The investigated `transition' to chaos in respect to N is different from the known phase transition near K=2 for s=2.

cond-mat.dis-nn↗

arXiv2008

Structural tendencies - Effects of adaptive evolution of complex (chaotic) systems

We describe systems using Kauffman and similar networks. They are directed funct ioning networks consisting of finite number of nodes with finite number of discr ete states evaluated in synchronous mode of discrete time. In this paper we introduce the notion and phenomenon of `structural tendencies'. Along the way we expand Kauffman networks, which were a synonym of Boolean netw orks, to more than two signal variants and we find a phenomenon during network g rowth which we interpret as `complexity threshold'. For simulation we define a simplified algorithm which allows us to omit the problem of periodic attractors. We estimate that living and human designed systems are chaotic (in Kauffman sens e) which can be named - complex. Such systems grow in adaptive evolution. These two simple assumptions lead to certain statistical effects i.e. structural tendencies observed in classic biology but still not explained and not investigated on theoretical way. E.g. terminal modifications or terminal predominance of additions where terminal means: near system outputs. We introduce more than two equally probable variants of signal, therefore our networks generally are not Boolean networks. T hey grow randomly by additions and removals of nodes imposed on Darwinian elimination. Fitness is defined on external outputs of system. During growth of the system we observe a phase transition to chaos (threshold of complexity) in damage spreading. Above this threshold we identify mechanisms of structural tendencies which we investigate in simulation for a few different networks types, including scale-free BA networks.

cond-mat.dis-nn↗