Matemática e Estatística | Capítulos/artigos em livros internacionais / Book chapters/papers in international books
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- Convergence to equilibria of solutions to the coagulation-fragmentation equationsPublication . Costa, Fernando Pestana daThe Coagulation-Fragmentation equations are a model for the dynamics of cluster growth and consist of a countable number of non-locally coupled ordinary differential equations, modelling the concentration of the various clusters. The framework for the study of these equations is to see them as a nonlinear ODE in an appropriate infinite dimensional Banach space. A number of results about existence, uniqueness, density conservation, and asymptotic behaviour of solutions have been obtained in recent years. In the present paper we review some of the more recent results on the asymptotic behaviour of solutions as time tends to infinity. We pay special attention to the different behaviour of solutions in the weak-star and in the strong topologies of the phase space. This distinction can be interpreted in terms of a dynamic phase transition in the physical system modelled by the equations. It is shown that a balance between the relative strength of coagulation and fragmentation is crucial for that distinct behaviour to take place.
- A fuzzy patient model in anaesthesiaPublication . Nunes, Catarina S.; Mahfouf, M.; Linkens, D. A.Balanced anaesthesia introduces the problem of drug interactions. In this article, the effect concentrations of anaesthetic and analgesic are used to model the pharmacodynamic interactions of the two drugs on the cardiovascular parameters, and on the auditory evoked potentials. An adaptive network-based fuzzy inference system is used to model the different signals. A stimulus model is used to establish the effects of surgical stimulus on the cardiovascular parameters. This model, is constructed into a Mamdani type of fuzzy model, using the anaesthetist knowledge described by fuzzy IF-THEN rules. Clinical data is used to construct the patient model.
- Garch models for drug effects on patient heart rate, during general anaesthesiaPublication . Brás, Susana; Nunes, Catarina S.; Amorim, PedroA model that can describe the effect of anaesthetic drugs on patient’s heart rate (HR) is of great importance when considering haemodynamic stability under surgery. A Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model was used to model HR considering the effect concentrations of the anaesthetic propofol and the analgesic remifentanil, using the clinical data of 16 patients. The model was able to capture the HR trend in all 16 patients with very small errors throughout the surgical time. A correlation was found between the GARCH parameters and patient baseline characteristics, leading to the possibility a patient adjusted adaptive model.
- Predictive adaptive control of the bispectral Index of the EEG (BIS): using the intravenous anaesthetic drug propofolPublication . Nunes, Catarina S.; Mendonça, Teresa F.; Magalhães, Hugo; Lemos, João M.; Amorim, PedroThe problem of controlling the level of unconsciousness measured by the Bispectral Index of the EEG (BIS) of patients under anaesthesia, is considered. It is assumed that the manipulated variable is the infusion rate of the hypnotic drug propofol, while the drug remifentanil is also administered for analgesia. Since these two drugs interact, the administration rate of remifentanil is considered as an accessible disturbance. In order to tackle the high uncertain present on the system, the predictive adaptive controller MUSMAR is used. The performance of the controller is illustrated by means of simulation with 45 patient individual adjusted models, which incorporate the effect of the drugs interaction on BIS. This controller structure proved to be robust to the remifentanil disturbance, different reference values and noise. A reduction of propofol consumption was also observed when comparing to the real clinical dose used for a similar BIS trend.
- Modelling drugs' pharmacodynamic interaction during general anaesthesia: the choice of pharmacokinetic modelPublication . Nunes, Catarina S.; Mendonça, Teresa F.; Antunes, Luís; Ferreira, David A.; Lobo, Francisco; Amorim, PedroThe effect of drugs’ interaction on the brain signal Bispectral Index (BIS) is of great importance for an anaesthesia control drug infusion system. In this study, two renowned pharmacokinetic (PK) models for propofol are compared, in order to evaluate its influence on the performance/predictably of a drug interaction model for BIS, considering data of 45 patients. The model was fitted per patient during anaesthesia induction, and tested for prediction under surgery. The results showed that the choice of PK model had influence on the overall performance. In the prediction phase, only one PK model presented good results with small errors.
- Intelligent control systems in anaesthesiaPublication . Mendonça, Teresa; Nunes, Catarina S.; Lago, Pedro
- Global dynamics of generic 3-flowsPublication . Araújo, Vítor; Bessa, Mário; Pacífico, Maria JoséIn this chapter we present some results from the generic viewpoint, either for C 1 flows on 3-manifolds, or for C1 conservative flows on 3-manifolds. This means that we present some properties satisfied by a generic subset of all vector fields in compact 3-manifolds in the C1 topology.
- Generic hamiltonian dynamical systems: an overviewPublication . Bessa, Mário; Dias, João LopesWe present for a general audience the state of the art on the generic properties of C 2 Hamiltonian dynamical systems.
- Area-preserving diffeomorphisms from the C1-StandpointPublication . Bessa, MárioMore than thirty years have passed since Newhouse (Am. J. Math. 99:1061–1087, 1977) published a dichotomy on C1 area-preserving diffeomorphisms. Here we revisit some central results on surface conservative C1-diffeomorphisms by presenting, in particular, a new proof of Newhouse’s theorem and also by proving some, although folklore, not yet proved results on this setting. We intend that this exposition can be used by a large audience as an introduction to the concept of dominated splitting and its relevance to the theory of C1-stability of area-preserving diffeomorphisms.
- Techniques in weak analysis for conservation resultsPublication . Fernandes, António; Ferreira, Fernando; Ferreira, GildaWe review and describe the main techniques for setting up systems of weak analysis, i.e. formal systems of second-order arithmetic related to subexponential classes of computational complexity. These involve techniques of proof theory (e.g., Herbrand’s theorem and the cut-elimination theorem) and model theoretic techniques like forcing. The techniques are illustrated for the particular case of polytime computability. We also include a brief section where we list the known results in weak analysis.
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