Non-Empirical Metrics for Ontology Visualizations Evaluation and Comparing

There are numerous ontology visualization systems, however, the choice of a visualization system is non-trivial, as there is no method for evaluation and comparing them, except for empirical experiments, that are subjective and costly. In this research, we aim to develop non- empirical metrics for ontology visualizations evaluation and comparing. First, we propose several half-formal metrics that require expert evaluation. These metrics are completeness, semanticity, and conservativeness. We apply the proposed metrics to evaluate and compare VOWL and Logic Graphs visualization systems. And second, we develop a com- pletely computable measure for the complexity of ontology visualizations, based on graph theory and information theory. In particular, ontology visualizations are considered as hypergraphs and the information mea- sure is derived from the Hartley function. The usage of the proposed information measure is exemplified by the evaluation of visualizations of the sample of axioms from the DoCO ontology in Logic Graphs and Graphol. These results can be practically applied for choosing ontology visualization systems in general and regarding a particular ontology.

Effective aspects of Bernoulli randomness

In this paper, we study Bernoulli random sequences, i.e. sequences that are Martin-Löf random with respect to a Bernoulli measure $\mu _p$ for some $p\in [0,1]$, where we allow for the possibility that $p$ is noncomputable. We focus in particular on the case in which the underlying Bernoulli parameter $p$ is proper (i.e. Martin-Löf random with respect to some computable measure). We show for every Bernoulli parameter $p$, if there is a sequence that is both proper and Martin-Löf random with respect to $\mu _p$, then $p$ itself must be proper, and explore further consequences of this result. We also study the Turing degrees of Bernoulli random sequences, showing, for instance, that the Turing degrees containing a Bernoulli random sequence do not coincide with the Turing degrees containing a Martin-Löf random sequence. Lastly, we consider several possible approaches to characterizing blind Bernoulli randomness, where the corresponding Martin-Löf tests do not have access to the Bernoulli parameter $p$, and show that these fail to characterize blind Bernoulli randomness.

RANK AND RANDOMNESS

We show that for each computable ordinal $\alpha > 0$ it is possible to find in each Martin-Löf random ${\rm{\Delta }}_2^0 $ degree a sequence R of Cantor-Bendixson rank α, while ensuring that the sequences that inductively witness R’s rank are all Martin-Löf random with respect to a single countably supported and computable measure. This is a strengthening for random degrees of a recent result of Downey, Wu, and Yang, and can be understood as a randomized version of it.

Conflict Fragmentation Index

It is widely accepted that fragmentation influences conflict processes in a profound way. Multi-party conflicts with several fronts are notoriously hard to resolve. However, there is no easily computable measure to approximate conflict fragmentation. In this article, we introduce the conflict fragmentation index (CFI), which is computed by adapting the Herfindahl–Hirschman index. The CFI considers the relative prominence of each dyadic-level conflict-fronts nested in the entire civil war. The relative prominence is approximated by using available information on conflict casualties. The CFI is time-variant and highly sensitive to battlefield dynamics. The flexibility of CFI can bring several advantages. Most notably, it is possible to calculate monthly or even daily measures of conflict fragmentation by taking state-based (government vs. NSA) as well as non-state based (NSA vs. NSA) conflicts into account. Overall, the CFI provides a theoretically-informed and easy to compute measure to approximate conflict fragmentation.

A Computable Measure of Algorithmic Probability by Finite Approximations with an Application to Integer Sequences

Given the widespread use of lossless compression algorithms to approximate algorithmic (Kolmogorov-Chaitin) complexity and that, usually, generic lossless compression algorithms fall short at characterizing features other than statistical ones not different from entropy evaluations, here we explore an alternative and complementary approach. We study formal properties of a Levin-inspired measure m calculated from the output distribution of small Turing machines. We introduce and justify finite approximations mk that have been used in some applications as an alternative to lossless compression algorithms for approximating algorithmic (Kolmogorov-Chaitin) complexity. We provide proofs of the relevant properties of both m and mk and compare them to Levin’s Universal Distribution. We provide error estimations of mk with respect to m. Finally, we present an application to integer sequences from the On-Line Encyclopedia of Integer Sequences, which suggests that our AP-based measures may characterize nonstatistical patterns, and we report interesting correlations with textual, function, and program description lengths of the said sequences.