Neutrosophic and Modal Components of Relations in Complex Systems

Semiotic components in the relations of complex systems depend on the Subject. There are two main semiotic components: Neutrosophic and Modal. Modal components are alethical and deontical. In this paper the authors applied the theory of Neutrosophy and Modal Logic to Deontical Impure Systems.

Generation of representation models for complex systems using Lagrangian functions

In this article, a new methodology is presented to obtain representation models for a priori relation z = u(x1, x2, . . . ,xn) (1), with a known an experimental dataset zi; x1i ; x2i ; x3i ; . . . ; xni i=1;2;...;p· In this methodology, a potential energy is initially defined over each possible model for the relationship (1), what allows the application of the Lagrangian mechanics to the derived system. The solution of the Euler–Lagrange in this system allows obtaining the optimal solution according to the minimal action principle. The defined Lagrangian, corresponds to a continuous medium, where a n-dimensional finite elements model has been applied, so it is possible to get a solution for the problem solving a compatible and determined linear symmetric equation system. The computational implementation of the methodology has resulted in an improvement in the process of get representation models obtained and published previously by the authors.

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.

A Finite Element Numerical Algorithm for Modelling and Data Fitting in Complex Systems

Numerical modelling methodologies are important by their application to engineering and scientific problems, because there are processes where analytical mathematical expressions cannot be obtained to model them. When the only available information is a set of experimental values for the variables that determine the state of the system, the modelling problem is equivalent to determining the hyper-surface that best fits the data. This paper presents a methodology based on the Galerkin formulation of the finite elements method to obtain representations of relationships that are defined a priori, between a set of variables: y = z(x1, x2,...., xd). These representations are generated from the values of the variables in the experimental data. The approximation, piecewise, is an element of a Sobolev space and has derivatives defined in a general sense into this space. The using of this approach results in the need of inverting a linear system with a structure that allows a fast solver algorithm. The algorithm can be used in a variety of fields, being a multidisciplinary tool. The validity of the methodology is studied considering two real applications: a problem in hydrodynamics and a problem of engineering related to fluids, heat and transport in an energy generation plant. Also a test of the predictive capacity of the methodology is performed using a cross-validation method.

Chebanov law and Vakar formula in mathematical models of complex systems

Ecological models written in a mathematical language L(M) or model language, with a given style or methodology can be considered as a text. It is possible to apply statistical linguistic laws and the experimental results demonstrate that the behaviour of a mathematical model is the same of any literary text of any natural language. A text has the following characteristics: (a) the variables, its transformed functions and parameters are the lexic units or LUN of ecological models; (b) the syllables are constituted by a LUN, or a chain of them, separated by operating or ordering LUNs; (c) the flow equations are words; and (d) the distribution of words (LUM and CLUN) according to their lengths is based on a Poisson distribution, the Chebanov's law. It is founded on Vakar's formula, that is calculated likewise the linguistic entropy for L(M). We will apply these ideas over practical examples using MARIOLA model. In this paper it will be studied the problem of the lengths of the simple lexic units composed lexic units and words of text models, expressing these lengths in number of the primitive symbols, and syllables. The use of these linguistic laws renders it possible to indicate the degree of information given by an ecological model.

Ideological Complex Systems: Mathematical Theory

The goal of this article is to build an abstract mathematical theory rather than a computational one of the process of transmission of ideology. The basis of much of the argument is Patten's Environment Theory that characterizes a system with its double environment (input or stimulus and output or response) and the existing interactions among them. Ideological processes are semiotic processes, and if in Patten's theory, the two environments are physical, in this theory ideological processes are physical and semiotic, as are stimulus and response.

“Unintended effects”: A theorem for complex systems

Unintended effects are well known to economists and sociologists and their consequences may be devastating. The main objective of this article is to formulate a mathematical theorem, based on Gödel's famous incompleteness theorem, in which it is shown, that from the moment deontical modalities (prohibition, obligation, permission, and faculty) are introduced into the social system, responses are allowed by the system that are not produced, however, prohibited responses or unintended effects may occur.

Some examples of modeling in chemical engineering: thermal treatment of polymers, phase equilibrium calculations and process design

Presentation submitted to PSE Seminar, Chemical Engineering Department, Center for Advanced Process Design-making (CAPD), Carnegie Mellon University, Pittsburgh (USA), October 2012.

Data analysis using circular causality in networks

Complex systems in causal relationships are known to be circular rather than linear; this means that a particular result is not produced by a single cause, but rather that both positive and negative feedback processes are involved. However, although interpreting systemic interrelationships requires a language formed by circles, this has only been developed at the diagram level, and not from an axiomatic point of view. The first difficulty encountered when analysing any complex system is that usually the only data available relate to the various variables, so the first objective was to transform these data into cause-and-effect relationships. Once this initial step was taken, our discrete chaos theory could be applied by finding the causal circles that will form part of the system attractor and allow their behavior to be interpreted. As an application of the technique presented, we analyzed the system associated with the transcription factors of inflammatory diseases.

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.

Enhancing QA systems with complex temporal question processing capabilities

This paper presents a multilayered architecture that enhances the capabilities of current QA systems and allows different types of complex questions or queries to be processed. The answers to these questions need to be gathered from factual information scattered throughout different documents. Specifically, we designed a specialized layer to process the different types of temporal questions. Complex temporal questions are first decomposed into simple questions, according to the temporal relations expressed in the original question. In the same way, the answers to the resulting simple questions are recomposed, fulfilling the temporal restrictions of the original complex question. A novel aspect of this approach resides in the decomposition which uses a minimal quantity of resources, with the final aim of obtaining a portable platform that is easily extensible to other languages. In this paper we also present a methodology for evaluation of the decomposition of the questions as well as the ability of the implemented temporal layer to perform at a multilingual level. The temporal layer was first performed for English, then evaluated and compared with: a) a general purpose QA system (F-measure 65.47% for QA plus English temporal layer vs. 38.01% for the general QA system), and b) a well-known QA system. Much better results were obtained for temporal questions with the multilayered system. This system was therefore extended to Spanish and very good results were again obtained in the evaluation (F-measure 40.36% for QA plus Spanish temporal layer vs. 22.94% for the general QA system).

Splitting complex temporal questions for question answering systems

This paper presents a multi-layered Question Answering (Q.A.) architecture suitable for enhancing current Q.A. capabilities with the possibility of processing complex questions. That is, questions whose answer needs to be gathered from pieces of factual information scattered in different documents. Specifically, we have designed a layer oriented to process the different types of temporal questions. Complex temporal questions are first decomposed into simpler ones, according to the temporal relationships expressed in the original question. In the same way, the answers of each simple question are re-composed, fulfilling the temporal restrictions of the original complex question. Using this architecture, a Temporal Q.A. system has been developed. In this paper, we focus on explaining the first part of the process: the decomposition of the complex questions. Furthermore, it has been evaluated with the TERQAS question corpus of 112 temporal questions. For the task of question splitting our system has performed, in terms of precision and recall, 85% and 71%, respectively.