Matemática e Estatística | Capítulos/artigos em livros internacionais / Book chapters/papers in international books
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- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Intelligent control systems in anaesthesiaPublication . Mendonça, Teresa; Nunes, Catarina S.; Lago, Pedro
- Microarray experiments on risk analysis using RPublication . Oliveira, Teresa A.; Oliveira, Amilcar; Monteiro, Andreia A.The microarray technique is a powerful biotechnological tool, expanding in a interesting way the vision with which issues in medicine are studied. Microarray technology, allows simultaneous evaluation of the expression of thousands of genes in different tissues of a given organism, and in different stages of development or environmental conditions. However, experiments with microarrays are still substantially costly and laborious, and as a consequence, they are usually conducted with relatively small sample sizes, thereby requiring a careful experimental design and statistical analysis. This paper adopts some applications of microarrays in risk analysis using R statistical software.
- Seasonal autoregressive integrated moving average time series model for tourism demand: the case of Sal Island, Cape VerdePublication . Neves, Gilberto A.; Nunes, Catarina S.; Fernandes, Paula OdeteThis article appears as an essential contribution for decision-makers in the Cape Verdean tourism sector given the impact that the number of overnight stays has on the economy of the country and the Sal Island, which until 2018 had been increasing every year. Since seasonality is a strong feature of the island's tourism, decision-makers are interested in knowing the seasonal variation in tourism demand. Thus, this study focused on the application of the Box-Jenkins method to the time series of the monthly number of nights stays in tourist establishments on the Sal Island, Cape Verde, over the period from January 2000 to December 2018, to find a model that better describes the series and with good forecast results for the year 2019. Several SARIMA models were studied using the Box-Jenkins method, with the SARIMA(1,1,1)(0,1,1)12 and the SARIMA(2,1,0)(0,1,1)12 demonstrating the best predictive performance in the test phase. However, in forecasting the series for the year 2019 the SARIMA(2,1,0)(0,1,1)12 achieved the best results with a MAPE=8.78%. This model can be used to simulate and analyse the number of overnight stays that be expected on the Island, if the tourism sector were not affected by the pandemic caused by COVID-19.
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