Guanglin Xu

A New Interpretation of the Determinant as Volume and Entropy

When V n 2 is the square of the n level of volume. When n = 0 we have zero order or point. When n = 1 we have the distance between two points. When n = 2 we have the surface of two dimensions. When n = 3 we have the volume. When n = 4 we have volume in the four dimensional space. At the level n we have volume in the n dimensional space.

Crossover and Permutation

We have two parents and two genes so we have the crossover \(ab,ba\) that are the terms of the permutation. For three parents and three genes we have the six possible crossovers from the three parents.

Database and Graph Theory

This book presents an introduction to morphogenetic computing [27–35]. The idea of morphogenetic computing came from conflicts and uncertainty situations that grow up when we compare two incompatible universes as local universe and global universe, neural universe and Boolean function universe, database sink and source incompatibility fuzzy logic in the many values.

Formal Description and References in Graph Theory

The first part is the start part and the second part is the final part. Now the first part is vector \(\left[ {\begin{array}{*{20}c} a \\ b \\ c \\ \end{array} } \right]\) the second part is the vector \(\left[ {\begin{array}{*{20}c} {(b,c)} \\ a \\ a \\ \end{array} } \right]\). Formally we can assume that the first vector is the values of coordinate e1 and the second vector is the values of the coordinates e2.

Neural Morphogenetic Computing and One Step Method

Systems design is the process of defining the architecture, components, modules, interfaces, and data for a system to satisfy specified requirements. One step back propagation is a method to design a neural network to satisfy specific Boolean function in output. This is and was the main problem in a percetron neural system and in the classical back propagation.

Morphogenetic and Morpheme Network to Structured Worlds

In Fig. 4.1 we show the chaotic structure of the language before the building of the network of morphology. Morphemes are the smallest meaningful parts of words and therefore represent a natural unit to study the evolution of words. Using a network approach from bioinformatics, we examine the historical dynamics of morphemes, the fixation of new morphemes and the emergence of words containing existing morphemes. We find that these processes are driven mainly by the number of different direct neighbors of a morpheme in words (connectivity, an equivalent to family size or type frequency) and not its frequency of usage (equivalent to token frequency).

Cycles, Sinks, Sources and Links Products

In Chap. 1, we have given the representation of relation with sinks and sources in database. In this chapter, we use a new instrument to give a method for modelling a graph with cycles, sinks and sources by the external product.

Morphogenetic Computing in Genetic Algorithms

For the multidimensional space S the transformation of vector X in this space is obtained by a quadratic matrix A.

Logic of Conflicts and Active Set with Uncertainty and Incoherence

An active set is a unifying space being able to act as a “bridge” for transferring information, ideas and results between distinct types of uncertainties and different types of applications. An active set is a set of agents who independently deliver true or false values for a given proposition. An active set is not a simple vector of logic values for different propositions, the results are a vector but the set is not. The difference between an ordinary set and active set is that the ordinary set has passive elements with values of the attributes defined by an external agent. In the active set, any element is an agent that internally defines the value of a given attribute for a passive element. Agents in the active set with a special criterion give the logic value for the same attribute. So agents in many cases are in a logic conflict and this generates semantic uncertainty on the logic evaluation. Criteria and agents are the two variables by which we give different logic values to the same attribute or proposition. Active set is beyond the modal logic.

Dynamic Database by Inconsistency and Morphogenetic Computing

Since Peter Chen published the article Entity---Relationship Modeling in 1976, Entity-Relationship database has become a hot spot for research. With the advent of the big data, it appears that Entity-Relationship database is substituted for attribute reduction map structure. In the big data we have no evidence of the relationship but only of attributes and maps. In this paper we give an attribute representation of the relationship. In fact we assume that any entity can be in two different attributes states with two different values. One is the attribute that sends a message that we denote as e1 and the other is to receive the message that we denote as e2. The values of the attributes are the names of the entities. A relationship is a superposition ae1i¾?+i¾?be2 of the two states. When we change the values of the states we change the database. When we change the two states in the same way we have isomorphism among database, and when we change the two states in different way we have isomorphism with distortion homotopic transformation. Given a set of independent data base we can generate compute all the other data base in a dynamical way. In this way we can reduce the database that we must memorize. Because we are interested in the generation of the form morphology of database we denote this new model of computation as morphogenetic computing.