Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds

2010 Mathematics Subject Classification: Primary: 37C85, 37A17, 37A45; Secondary: 11K36, 11L07.

Genetic regulatory mechanisms by means of extended interactive Petri nets

In our work we have chosen to integrate formalism for knowledge representation with formalism for process representation as a way to specify and regulate the overall activity of a multi-cellular agent. The result of this approach is XP,N, another formalism, wherein a distributed system can be modeled as a collection of interrelated sub-nets sharing a common explicit control structure. Each sub-net represents a system of asynchronous concurrent threads modeled by a set of transitions. XP,N combines local state and control with interaction and hierarchy to achieve a high-level abstraction and to model the complex relationships between all the components of a distributed system. Viewed as a tool XP,N provides a carefully devised conflict resolution strategy that intentionally mimics the genetic regulatory mechanism used in an organic cell to select the next genes to process.

Hierarchical modelling of timber reference properties using probabilistic methods: Maximum Likelihood Method, Bayesian Methods and Probability Networks

In recent decades, an increased interest has been evidenced in the research on multi-scale hierarchical modelling in the field of mechanics, and also in the field of wood products and timber engineering. One of the main motivations for hierar-chical modelling is to understand how properties, composition and structure at lower scale levels may influence and be used to predict the material properties on a macroscopic and structural engineering scale. This chapter presents the applicability of statistic and probabilistic methods, such as the Maximum Likelihood method and Bayesian methods, in the representation of timber’s mechanical properties and its inference accounting to prior information obtained in different importance scales. These methods allow to analyse distinct timber’s reference properties, such as density, bending stiffness and strength, and hierarchically consider information obtained through different non, semi or destructive tests. The basis and fundaments of the methods are described and also recommendations and limitations are discussed. The methods may be used in several contexts, however require an expert’s knowledge to assess the correct statistic fitting and define the correlation arrangement between properties.