Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e. g., fractional Brownian motion, Levy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation sigma t which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

A UML profile for the OBO relation ontology

Background: Ontologies have increasingly been used in the biomedical domain, which has prompted the emergence of different initiatives to facilitate their development and integration. The Open Biological and Biomedical Ontologies (OBO) Foundry consortium provides a repository of life-science ontologies, which are developed according to a set of shared principles. This consortium has developed an ontology called OBO Relation Ontology aiming at standardizing the different types of biological entity classes and associated relationships. Since ontologies are primarily intended to be used by humans, the use of graphical notations for ontology development facilitates the capture, comprehension and communication of knowledge between its users. However, OBO Foundry ontologies are captured and represented basically using text-based notations. The Unified Modeling Language (UML) provides a standard and widely-used graphical notation for modeling computer systems. UML provides a well-defined set of modeling elements, which can be extended using a built-in extension mechanism named Profile. Thus, this work aims at developing a UML profile for the OBO Relation Ontology to provide a domain-specific set of modeling elements that can be used to create standard UML-based ontologies in the biomedical domain. Results: We have studied the OBO Relation Ontology, the UML metamodel and the UML profiling mechanism. Based on these studies, we have proposed an extension to the UML metamodel in conformance with the OBO Relation Ontology and we have defined a profile that implements the extended metamodel. Finally, we have applied the proposed UML profile in the development of a number of fragments from different ontologies. Particularly, we have considered the Gene Ontology (GO), the PRotein Ontology (PRO) and the Xenopus Anatomy and Development Ontology (XAO). Conclusions: The use of an established and well-known graphical language in the development of biomedical ontologies provides a more intuitive form of capturing and representing knowledge than using only text-based notations. The use of the profile requires the domain expert to reason about the underlying semantics of the concepts and relationships being modeled, which helps preventing the introduction of inconsistencies in an ontology under development and facilitates the identification and correction of errors in an already defined ontology.