Comments on ‘‘Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions

Applied Mathematical Modelling, Vol.33

Constraint reasoning for differential models

The basic motivation of this work was the integration of biophysical models within the interval constraints framework for decision support. Comparing the major features of biophysical models with the expressive power of the existing interval constraints framework, it was clear that the most important inadequacy was related with the representation of differential equations. System dynamics is often modelled through differential equations but there was no way of expressing a differential equation as a constraint and integrate it within the constraints framework. Consequently, the goal of this work is focussed on the integration of ordinary differential equations within the interval constraints framework, which for this purpose is extended with the new formalism of Constraint Satisfaction Differential Problems. Such framework allows the specification of ordinary differential equations, together with related information, by means of constraints, and provides efficient propagation techniques for pruning the domains of their variables. This enabled the integration of all such information in a single constraint whose variables may subsequently be used in other constraints of the model. The specific method used for pruning its variable domains can then be combined with the pruning methods associated with the other constraints in an overall propagation algorithm for reducing the bounds of all model variables. The application of the constraint propagation algorithm for pruning the variable domains, that is, the enforcement of local-consistency, turned out to be insufficient to support decision in practical problems that include differential equations. The domain pruning achieved is not, in general, sufficient to allow safe decisions and the main reason derives from the non-linearity of the differential equations. Consequently, a complementary goal of this work proposes a new strong consistency criterion, Global Hull-consistency, particularly suited to decision support with differential models, by presenting an adequate trade-of between domain pruning and computational effort. Several alternative algorithms are proposed for enforcing Global Hull-consistency and, due to their complexity, an effort was made to provide implementations able to supply any-time pruning results. Since the consistency criterion is dependent on the existence of canonical solutions, it is proposed a local search approach that can be integrated with constraint propagation in continuous domains and, in particular, with the enforcing algorithms for anticipating the finding of canonical solutions. The last goal of this work is the validation of the approach as an important contribution for the integration of biophysical models within decision support. Consequently, a prototype application that integrated all the proposed extensions to the interval constraints framework is developed and used for solving problems in different biophysical domains.

Toxicity of carcinogenic and non-carcinogenic Polycyclic Aromatic Hydrocarbons and their mixtures to aquatic organisms under ecologically-relevant scenarios

Polycyclic aromatic hydrocarbons (PAHs) are ubiquitous priority pollutants that tend to be trapped in aquatic sediments due to their high hydrophobicity. Nonetheless, the differential toxicological effects and mechanisms between the various classes of PAHs and their mixtures, as they invariably occur in the environment, are scarcely known, especially under ecologically-relevant scenarios. This thesis aimed at establishing a bridge between the study of mechanistic pathways and environmental monitoring of carcinogenic and non-carcinogenic PAHs, by introducing ecological-relevance in the research with model PAHs. A first bioassay conducted in situ with the mussel Mytilus edulis demonstrated that, dredging operations in harbours increase PAH bioavailability, eliciting genotoxicity, and showed that established environmental guidelines underestimate risk. Subsequent ex situ bioassays were performed with the carcinogenic benzo[b]fluoranthene (B[b]F) and non-carcinogenic phenantrene (Phe), selected following preceding results, and revealed that low-moderate concentrations of these PAHs in spiked sediments induce genotoxic effects to the clam Ruditapes decussatus, therefore contradicting the general notion that bivalves are less sensitive to PAHs than vertebrates due to inefficient bioactivation. Also, it was demonstrated that passive samplers permit inferring on PAH bioavailability but not on bioaccumulation or toxic effects. On the other hand, sea basses (Dicentrarchus labrax), yielded a complex pattern of effects and responses, relatively to genotoxicity, oxidative stress and production of specific metabolites, especially when exposed to mixtures of the PAHs which led to additive, if not synergistic, effects. It was shown that Phe may elicit significant genotoxicity especially in presence of B[b]F, even though the low, albeit realistic, exposure concentrations diluted dose- and time-independent relationships. The present work demonstrated that environmental quality guidelines underestimate the effects of PAHs in realistic scenarios and showed that the significant genotoxic and histopathological effects caused by mixed PAHs may not be reflected by oxidative stress- or CYP-related biomarkers. Besides important findings on the metabolism of PAH mixtures, the work calls for the need to re-evaluate the criteria for assessing risk and for the disclosure of more efficient indicators of toxicological hazard.