An introduction to alysidal algebra (V): phenomenological components

Purpose – This paper aims to refer to a subjective approach to a type of complex system: human ecosystems, referred to as deontical impure systems (DIS) to capture a set of properties fundamental to the distinction between human and natural ecosystems. There are four main phenomenological components: directionality, intensity, connection energy and volume. The paper establishes thermodynamics of deontical systems based on the Law of Zipf and the temperature of information. Design/methodology/approach – Mathematical and logical development of human society structure. Findings – A fundamental question in this approach to DIS is the intensity or forces of a relation. Concepts are introduced as the system volume and propose a system thermodynamic theory. It hints at the possibility of adapting the fractal theory by introducing the fractal dimension of the system. Originality/value – This paper is a continuation of other previous papers and developing the theory of DIS.

Diversity for Texts Builds in Language L(MT) II: Indexes Based in Abundances

One saw previously that indications of diversity IT and the one of Shannon permits to characterize globally by only one number one fundamental aspects of the text structure. However a more precise knowledge of this structure requires specific abundance distributions and the use, to represent this one, of a suitable mathematical model. Among the numerous models that would be either susceptible to be proposed, the only one that present a real convenient interest are simplest. One will limit itself to study applied three of it to the language L(MT): the log-linear, the log-normal and Mac Arthur's models very used for the calculation of the diversity of the species of ecosystems, and used, we believe that for the first time, in the calculation of the diversity of a text written in a certain language, in our case L(MT). One will show advantages and inconveniences of each of these model types, methods permitting to adjust them to text data and in short tests that permit to decide if this adjustment is acceptable.