Introduction to Coding Theory for Flow Equations of Complex Systems Models

The modeling of complex dynamic systems depends on the solution of a differential equations system. Some problems appear because we do not know the mathematical expressions of the said equations. Enough numerical data of the system variables are known. The authors, think that it is very important to establish a code between the different languages to let them codify and decodify information. Coding permits us to reduce the study of some objects to others. Mathematical expressions are used to model certain variables of the system are complex, so it is convenient to define an alphabet code determining the correspondence between these equations and words in the alphabet. In this paper the authors begin with the introduction to the coding and decoding of complex structural systems modeling.

Disipation Functions of Flow Equations in Models of Complex Systems

In an open system, each disequilibrium causes a force. Each force causes a flow process, these being represented by a flow variable formally written as an equation called flow equation, and if each flow tends to equilibrate the system, these equations mathematically represent the tendency to that equilibrium. In this paper, the authors, based on the concepts of forces and conjugated fluxes and dissipation function developed by Onsager and Prigogine, they expose the following hypothesis: Is replaced in Prigogine’s Theorem the flow by its equation or by a flow orbital considering conjugate force as a gradient. This allows to obtain a dissipation function for each flow equation and a function of orbital dissipation.

Syntactic and Semantic Relationships in Models of Complex Systems: An Ecological Case

In this paper, the authors extend and generalize the methodology based on the dynamics of systems with the use of differential equations as equations of state, allowing that first order transformed functions not only apply to the primitive or original variables, but also doing so to more complex expressions derived from them, and extending the rules that determine the generation of transformed superior to zero order (variable or primitive). Also, it is demonstrated that for all models of complex reality, there exists a complex model from the syntactic and semantic point of view. The theory is exemplified with a concrete model: MARIOLA model.

Trends in mortality due to motor vehicle traffic accident injuries between 1987 and 2011 in a Spanish region (Comunitat Valenciana)

Objective: To analyse the time evolution of the rates of mortality due to motor vehicle traffic accidents (MVTA) injuries that occurred among the general population of Comunitat Valenciana between 1987 and 2011, as well as to identify trend changes by sex and age group. Methods: An observational study of annual mortality trends between 1987 and 2011. We studied all deaths due to MVTA injuries that occurred during this period of time among the non-institutionalised population residing in Comunitat Valenciana (a Spanish Mediterranean region that had a population of 5,117,190 inhabitants in 2011). The rates of mortality due to MVTA injuries were calculated for each sex and year studied. These rates were standardised by age for the total population and for specific age groups using the direct method (age-standardised rate – ASR). Joinpoint regression models were used in order to detect significant trend changes. Additionally, the annual percentage change (APC) of the ASRs was calculated for each trend segment, which is reflected in statistically significant joinpoints. Results: For all ages, ASRs decrease greatly in both men and women (70% decrease between 1990 and 2011). In 1990 and 2011, men have rates of 36.5 and 5.2 per 100,000 men/year, respectively. In the same years, women have rates of 8.0 and 0.9 per 100,000 women/year, respectively. This decrease reaches up to 90% in the age group 15–34 years in both men and women. ASR ratios for men and women increased over time for all ages: this ratio was 3.9 in 1987; 4.6 in 1990; and 5.8 in 2011. For both men and women, there is a first significant segment (p < 0.05) with an increasing trend between 1987 and 1989–1990. After 1990, there are 3 segments with a significant decreasing APC (1990–1993, 1993–2005 and 2005–2011, in the case of men; and 1989–1996, 1999–2007 and 2007–2011, in the case of women). Conclusion: The risk of death due to motor vehicle traffic accidents injuries has decreased significantly, especially in the case of women, for the last 25 years in Comunitat Valenciana, mainly as of 2006. This may be a consequence of the road-safety measures that have been implemented in Spain and in Comunitat Valenciana since 2004. The economic crisis that this country has undergone since 2008 may have also been a contributing factor to this decrease. Despite the decrease, ASR ratios for men and women increased over time and it is still a high-risk cause of death among young men. It is thus important that the measures that helped decrease the risk of death are maintained and improved over time.