Entropy bounds for hierarchical molecular networks

In this paper we derive entropy bounds for hierarchical networks. More precisely, starting from a recently introduced measure to determine the topological entropy of non-hierarchical networks, we provide bounds for estimating the entropy of hierarchical graphs. Apart from bounds to estimate the entropy of a single hierarchical graph, we see that the derived bounds can also be used for characterizing graph classes. Our contribution is an important extension to previous results about the entropy of non-hierarchical networks because for practical applications hierarchical networks are playing an important role in chemistry and biology. In addition to the derivation of the entropy bounds, we provide a numerical analysis for two special graph classes, rooted trees and generalized trees, and demonstrate hereby not only the computational feasibility of our method but also learn about its characteristics and interpretability with respect to data analysis

Entropy Bounds for Hierarchical Molecular Networks

In this paper we derive entropy bounds for hierarchical networks. More precisely, starting from a recently introduced measure to determine the topological entropy of non-hierarchical networks, we provide bounds for estimating the entropy of hierarchical graphs. Apart from bounds to estimate the entropy of a single hierarchical graph, we see that the derived bounds can also be used for characterizing graph classes. Our contribution is an important extension to previous results about the entropy of non-hierarchical networks because for practical applications hierarchical networks are playing an important role in chemistry and biology. In addition to the derivation of the entropy bounds, we provide a numerical analysis for two special graph classes, rooted trees and generalized trees, and demonstrate hereby not only the computational feasibility of our method but also learn about its characteristics and interpretability with respect to data analysis

Symbolic Abstraction of System Requirements

Because aerospace systems become more and more complex, the pile of documents specifying the requirements for such systems grows continuously. It is obvious that it is not enough just to produce more documents. The expressiveness of system requirements has to be considered as well. However, the ambiguity of natural language generally used to define requirements impedes a manageable growth of system complexities. Therefore, new approaches of abstraction and formalization are needed. In this paper, we describe a semi-automatic implementation of symbolic abstraction by using methods of natural language processing and temporal logic. A graphical presentation of grammatical relations supports the comprehensibility of symbolic abstraction whereas methods defined by the Linear Temporal Logic (LTL) are incorporated to specify the temporal order of requirements. We demonstrate our approach by using exemplary requirements for the ExoMars mission

Characterizing Classes of Structured Objects by Means of Information Inequalities

The problem to characterize and investigate structured objects by using information theory is currently of considerable interest. In this paper, we describe a method for characterizing structured objects representing graphs by means of information inequalities. For this, we deal with information inequalities which describe relations between information measures for graphs. Additionally, we sketch an approach for comparing such information measures qualitatively.