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The purpose of this paper is the study of the causal relationship. The concept called “naive” causality can be stated more generally as the belief (or knowledge) that results follow actions, and that these results are not random, but are consistently linked with causes. The authors have thus formed a very general and precarious concept of causality, but one that appropriately reflects the meaning of causality at the level of common sense.

Mathematical and logical development of the causality in complex systems.

There are three aspects of rationality that give the human mind a unique vision of reality: quantification: reduction of phenomena to quantitative terms; cause and effect: causal relationship, which allows predicting; and the necessary and valid use of (deterministic) mechanical models. This work is dedicated to the second aspect, that of causality, but at present leaves aside the discussion of possibility-necessity, proposing a modification to philosophical synthesis of causality specified by Bunge (1959), with contributions made by Patten et al. (1976) and LeShan and Margenau (1982).

Causality is an epistemological category, because it concerns the experience and knowledge of the human subject, without being necessarily a property of reality.

The purpose of this paper is to demonstrate mathematically the impossibility of achieving a utopian society. Demonstrate that any attempt to correct deviations from a hypothetical trajectory whose ultimate goal is the utopia, increasingly demands more work, including measures that lead to terror, which may even be absolute, leading to the horrible paradox that in seeking paradise hell is constructed.

Scientific tools that the authors have used are: the theory of the system linkage, alysidal algebra, kinematic theory and vector analysis.

Myths are the substrate of some complex systems of beliefs and utopia is its ultimate goal. The use of the combination of the theory of trajectories, belonging to the alysidal algebra, the theorem of unintended effects and kinematics theory provides an approximation to deviations suffering utopian ideological currents and their corrections.

This paper is a continuation of other previous papers developing the theory of complex societies.

The purpose of this paper is to show that transmission of information and information storage or registration depends on structures. Structures emerge from coordinated sets of constraints. Complex systems depend on their structures to function. The temporal sequence of changes in the levels of the complex system determines its behavior. These three concepts are intimately linked with the environment. Environment, structure, function and behavior form a complex system–environment unit, which is the operational unit of existence for all open complex systems. Therefore, it becomes a point in the directional propagation of the cause, where stimulus environment becomes a Creaon, and then the Creaon becomes a Genon, becoming in turn the response to the experienced environment. The formation of structures is the main phenomenon of evolution. Evolution can also be accepted as free, in the sense that it does not cost additional deaths.

Mathematical and logical development of the structure and thermodynamics in complex systems.

Based on the above considerations, the authors are going to introduce two fundamental principles in Complex systems Theory: the Matthew Effect and the Principle of Sagan.

But as the authors’ purpose is to give a formal definition of a complex system from a totally theoretical point of view, they establish a relationship between concepts of General Systems Theory, Theory of the Environment, linguistics, Information Theory and thermodynamics.

The purpose of this paper is to propose a mathematical model to determine invariant sets, set covering, orbits and, in particular, attractors in the set of tourism variables. Analysis was carried out based on an algorithm and applying an interpretation of chaos theory developed in the context of General Systems Theory and Big Data.

Tourism is one of the most digitalized sectors of the economy, and social networks are an important source of data for information gathering. However, the high levels of redundant information on the Web and the appearance of contradictory opinions and facts produce undesirable effects that must be cross-checked against real data. This paper sets out the causal relationships associated with tourist flows to enable the formulation of appropriate strategies.

The results can be applied to numerous cases, for example, in the analysis of tourist flows, these findings can be used to determine whether the behaviour of certain groups affects that of other groups, as well as analysing tourist behaviour in terms of the most relevant variables.

The technique presented here breaks with the usual treatment of the tourism topics. Unlike statistical analyses that merely provide information on current data, the authors use orbit analysis to forecast, if attractors are found, the behaviour of tourist variables in the immediate future.

This paper aims to describe to the dependence and independence functions associated with the system and the environment system, as also the interdependence functions between the two systems.

These functions, like the connections between pairs of entities in the systems, are formulated using the derivative concept. The system will thus be analysed in function of processes between mathematically formulated variables.

For each entity in the system or in the environment system it will be possible to determine networks of dependence and interdependence, which will be represented by their associated functions.

The functions described in this paper aim to decipher the processes that occur in systems. The characterisation of these functions via derivates implies an acknowledgement of the processes in the system, given that by simply observing the value of the derivatives obtained, one can uncover the network of interdependences between system entities.

Considers that as a general rule metrics serve to compare elements in the same set, such as the Euclidean metric by means of which we can calculate the distance between points ℜ ², ℜ³ etc. In practical applications such as in the biological sciences, it is necessary to compare cells which may have identical or different numbers of genes. Suggests that we may wish to compare different genes formed of finite sequences of four nucleotides. These are genes which may have the same or different numbers of bases. These and other questions are analysed from the viewpoint of general systems theory.

In systems theory, authors such as Klir, Miller, Yang, Lin and Ma, Backlund, etc. have developed different definitions of the system concept in function of both the type of variables used and the type of connection between variables. The concept of the subsystem, however, tends not to vary substantially from author to author, and this leads to a new system definition based on the subsystem concept, analysing the possible cases of interaction between subsystems and obtaining results for the overall system from an analysis of its subsystems.

Based on some of the results and definitions provided in the paper “system linkage: structural functions and hierarchies” and adding new definitions that are in keeping with the spirit of the same paper, new results have been obtained that explore the utility of the structural input‐output function.

Our approach is based principally on the application of graph theory to the study of relationships between variables using specific set theory concepts.

A result such as the fact that A covers B, for example, can be interpreted in terms of the latter set being formed of direct influences from elements in the former set in relation to one or more than one relationships. Analogously, the invariant set concept may be interpreted as the set maintaining its structure and status, remaining constant with respect to any possible relationships.

From a practical point of view, in the context of the study of networks within an ecosystem, authors (such as Patten et al. and Patten) have demonstrated that indirect effects between the variables of an ecosystem outweigh direct effects. This is the notion that the present authors have borne in mind in order to extend previous results to indirect influences from a discrete perspective.

Describes issues relevant to multilevel systems and, as a particular case, living systems analysed from the entities point of view. As attributes, behaviours, sub‐systems, etc., entities are primitive terms. For this reason, in examining issues such as the influences between entities, look indirectly at issues referring to different levels in the system. This notion was also extended in considering the environment system and analysing the different relationships between the system and the environment system.

Not all cells are equal: each tissue and organ has its own type of cell. Although the nucleus of each cell in a living system has the same genetic information, each one dispenses of the lion's share of that information and only those genes that are necessary for carrying out the function of the particular organ or tissue to which they belong remain active. Despite the fact that in specific scientific fields, such as ecosystem studies, it is possible to measure the relationships between different variables and to compare the various direct and indirect effects they may have on one another, there has been no such development in the wider context of a General Systems Theory. This paper sets out to address the question of cellular change by interpreting processes such as direct and indirect causality, cellular meiosis and mutation of cells.