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- Generalized models from Beta(p,2) densities with strong allee effect: dynamical approachPublication . Aleixo, Sandra; Rocha, J. LeonelA dynamical approach to study the behaviour of generalized populational growth models from Bets(p, 2) densities, with strong Allee effect, is presented. The dynamical analysis of the respective unimodal maps is performed using symbolic dynamics techniques. The complexity of the correspondent discrete dynamical systems is measured in terms of topological entropy. Different populational dynamics regimes are obtained when the intrinsic growth rates are modified: extinction, bistability, chaotic semistability and essential extinction.
- An Extension of Gompertzian Growth Dynamics Weibull and Frechet ModelsPublication . Rocha, J. Leonel; Aleixo, SandraIn this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.
- Characterization of gastric cells infection by diverse Helicobacter pylori strains through Fourier-transform infrared spectroscopyPublication . Marques, Vanda; Ribeiro Da Cunha, Bernardo; Couto, Andreia; Sampaio, Pedro; Fonseca, Luís P. P.; Aleixo, Sandra; Calado, CecíliaThe infection of Helicobacter pylori, covering 50% of the world-population, leads to diverse gastric diseases as ulcers and cancer along the life-time of the human host. To promote the discovery of biomarkers of bacterial infection, in the present work, Fourier-transform infrared spectra were acquired from adenocarcinoma gastric cells, incubated with H. pylori strains presenting different genotypes concerning the virulent factors cytotoxin associated gene A and vacuolating cytotoxin A. Defined absorbance ratios were evaluated by diverse methods of statistical inference, according to the fulfillment of the tests assumptions. It was possible to define from the gastric cells, diverse absorbance ratios enabling to discriminate: i) The infection; ii) the bacteria genotype; and iii) the gastric disease of the patients from which the bacteria were isolated. These biomarkers could fasten the knowledge of the complex infection process while promoting a platform for a new diagnostic method, rapid but also specific and sensitive towards the diagnosis of both infection and bacterial virulence.
- Synchronization in Von Bertalanffy’s modelsPublication . Rocha, J. Leonel; Aleixo, Sandra; Caneco, AcilinaMany data have been useful to describe the growth of marine mammals, invertebrates and reptiles, seabirds, sea turtles and fishes, using the logistic, the Gom-pertz and von Bertalanffy's growth models. A generalized family of von Bertalanffy's maps, which is proportional to the right hand side of von Bertalanffy's growth equation, is studied and its dynamical approach is proposed. The system complexity is measured using Lyapunov exponents, which depend on two biological parameters: von Bertalanffy's growth rate constant and the asymptotic weight. Applications of synchronization in real world is of current interest. The behavior of birds ocks, schools of fish and other animals is an important phenomenon characterized by synchronized motion of individuals. In this work, we consider networks having in each node a von Bertalanffy's model and we study the synchronization interval of these networks, as a function of those two biological parameters. Numerical simulation are also presented to support our approaches.
- Towards an automated statistical workflow for biomarker screening in Fourier-transform infrared spectroscopyPublication . Ribeiro Da Cunha, Bernardo; Aleixo, Sandra; Fonseca, Luís P.; Calado, CecíliaThe increasing availability and sensitivity of analytical technologies has resulted in much higher complexity of molecular and cellular data, which biomarkers facilitate the bridge with a given biological state under scrutiny. Importantly, biomarkers are critical in spectroscopic technologies, as is the case of Fourier-transform infrared spectroscopy, for which different approaches to identify biomarkers have been established, for instance univariate statistical hypothesis tests. A workflow for the automatic application of said statistical tests is proposed with the objective of enabling a high throughput screening-approach that ensures statistical robustness, and works in a user-independent manner, thereby reducing analysis bias. The proposed workflow is the first step towards an automated method for biomarker screening, thus it is limited to distinguishing two populations. Firstly, the method used in previous work was improved to ensure the most powerful and accurate statistical tests are applied. Then, the statistical workflow was generalized to a more comprehensive range of data sets of two populations, for instance when sample size is not deemed high (less than thirty observations). Lastly, future work is outlined regarding the extension of the workflow to cases with more than two populations, but also of methods that can increase the pool of putative biomarkers that will then be screened for statistical significance.
- A spatial econometric analysis of the calls to the Portuguese National Health LinePublication . Simões, Paula; Carvalho, M. Lucília; Aleixo, Sandra; Gomes, Sérgio; Natário, IsabelThe Portuguese National Health Line, LS24, is an initiative of the Portuguese Health Ministry which seeks to improve accessibility to health care and to rationalize the use of existing resources by directing users to the most appropriate institutions of the national public health services. This study aims to describe and evaluate the use of LS24. Since for LS24 data, the location attribute is an important source of information to describe its use, this study analyses the number of calls received, at a municipal level, under two different spatial econometric approaches. This analysis is important for future development of decision support indicators in a hospital context, based on the economic impact of the use of this health line. Considering the discrete nature of data, the number of calls to LS24 in each municipality is better modelled by a Poisson model, with some possible covariates: demographic, socio-economic information, characteristics of the Portuguese health system and development indicators. In order to explain model spatial variability, the data autocorrelation can be explained in a Bayesian setting through different hierarchical log-Poisson regression models. A different approach uses an autoregressive methodology, also for count data. A log-Poisson model with a spatial lag autocorrelation component is further considered, better framed under a Bayesian paradigm. With this empirical study we find strong evidence for a spatial structure in the data and obtain similar conclusions with both perspectives of the analysis. This supports the view that the addition of a spatial structure to the model improves estimation, even in the case where some relevant covariates have been included.
- Weighted coefficients to measure agreement among several sets of ranks emphasizing top and bottom ranks at the same timePublication . Aleixo, Sandra; Teles, JúliaIn this paper, two new weighted coefficients of agreement to measure the concordance among several (more than two) sets of ranks, putting more weight in the lower and upper ranks simultaneously, are presented. These new coefficients, the signed Klotz and the signed Mood, generalize the correspondent rank-order coefficients to measure the agreement between two sets of ranks previously proposed by the authors [1]. Under the null hypothesis of no agreement or no association among the rankings, the asymptotic distribution of these new coefficients was derived. To illustrate the worth of these measures, an example is presented to compare them with the Kendall’s coefficient and the van der Waerden correlation coefficient.
- Dynamical behaviour on the parameter space: new populational growth models proportional to beta densitiesPublication . Aleixo, Sandra; Rocha, J. Leonel; Pestana, Dinis D.We present new populational growth models, generalized logistic models which are proportional to beta densities with shape parameters p and 2, where p > 1, with Malthusian parameter r. The complex dynamical behaviour of these models is investigated in the parameter space (r, p), in terms of topological entropy, using explicit methods, when the Malthusian parameter r increases. This parameter space is split into different regions, according to the chaotic behaviour of the models.
- Weighting lower and upper ranks simultaneously through rank-order correlation coefficientsPublication . Aleixo, Sandra; Teles, JuliaTwo new weighted correlation coefficients, that allow to give more weight to the lower and upper ranks simultaneously, are proposed. These indexes were obtained computing the Pearson correlation coefficient with a modified Klotz and modified Mood scores. Under the null hypothesis of independence of the two sets of ranks, the asymptotic distribution of these new coefficients was derived. The exact and approximate quantiles were provided. To illustrate the value of these measures an example, that could mimic several biometrical concerns, is presented. A Monte Carlo simulation study was carried out to compare the performance of these new coefficients with other weighted coefficient, the van der Waerden correlation coefficient, and with two non-weighted indexes, the Spearman and Kendall correlation coefficients. The results show that, if the aim of the study is the detection of correlation or agreement between two sets of ranks, putting emphasis on both lower and upper ranks simultaneously, the use of van der Waerden, signed Klotz and signed Mood rank-order correlation coefficients should be privileged, since they have more power to detect this type of agreement, in particular when the concordance was focused on a lower proportion of extreme ranks. The preference for one of the coefficients should take into account the weight one wants to assign to the extreme ranks.
- Impact of the human mesenchymal stem cells donor on conditional medium compositionPublication . Pereira, Maria João Canha; Ramalhete, Luís; Aleixo, Sandra; da Silva, Cláudia L.; Cabral, Joaquim M.S.; Calado, Cecília; Fernandes, AnaExosomes produced by Mesenchymal Stem Cells (MSCs) can represent a very appealing strategy for cell-free therapies. However, to achieve this reality it is necessary to further understand the process associated to the MSC culture when conditioned to produce exosomes. In the present work, it was evaluated how different MSC obtained from different donors may affect the conditioned media composition and how this can be influenced by the conditioned media type (DMEM versus Xeno-Free medium, XF). The molecular fingerprint of the conditioned media composition was obtained by mid-infrared (MIR) spectroscopy, as this technique reflects fundamental vibrations of a high diversity of functional chemical groups present in biological samples. It was observed by principal component analysis of the second derivative spectra of conditioned media that the media chemical composition depends more from the MSCs donor than the conditioning days. Diverse spectral regions, characteristic of defined chemical groups, enabled to discriminate the chemical composition of the media according to the MSC donor. All of this was observed in both types of media (DMEM and XF). This work is a step forward to understand how different MSC donors and conditioned media may affect the exosomes characteristics.