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- Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approachPublication . Sardanyés, Josep; Rodrigues, Carla; Januário, Cristina; Martins, Nuno; Gil-Gómez, Gabriel; Duarte, JorgeIn this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems – the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, showing that an increased activation makes the system to enter into chaotic dynamics via a period-doubling bifurcation scenario. Then, by adding demographic stochasticity into the homotopy solutions, we show, as a difference from the deterministic dynamics, that an increased activation of the immune cells facilitates cancer clearance involving tumor cells extinction and healthy cells persistence. Our results highlight the importance of therapies activating the effector immune cells at early stages of cancer progression.
- Active vibration attenuation in viscoelastic laminated composite panels using multiobjective optimizationPublication . Luís, Ndilokelwa F.; Madeira, JFA; Araújo, A. L.; Ferreira, A. J. M.The optimal design of viscoelastic laminated composite panels with active piezoelectric patches is addressed in this paper. Constrained optimization is conducted to determine optimal distributions of piezoelectric patches on the top and bottom surfaces of laminated plates with viscoelastic layers. The design variables are the number and position of these patches, and the objectives are the minimization of the number of patches, the maximization of the fundamental modal loss factor and the maximization of the fundamental natural frequency. The problem is solved using the Direct MultiSearch (DMS) solver for derivative-free MultiObjective Optimization (MOO). The objective functions are evaluated by a finite element model that was developed for laminated sandwich plates incorporating piezoelectric or viscoelastic layers. Trade-off Pareto optimal fronts and the respective optimal active patch configurations are obtained and the results are analyzed and discussed.
- Algebraic structure for interaction on mixed modelsPublication . Ramos, Paulo; Fernandes, Célia; Mexia, João TiagoBinary operations on commutative Jordan algebras, CJA, can be used to study interactions between sets of factors belonging to a pair of models in which one nests the other. It should be noted that from two CJA we can, through these binary operations, build CJA. So when we nest the treatments from one model in each treatment of another model, we can study the interactions between sets of factors of the first and the second models.
- Algebraic structure for the crossing of balanced and stair nested designsPublication . Fernandes, Célia; Ramos, Paulo; Mexia, João TiagoStair nesting allows us to work with fewer observations than the most usual form of nesting, the balanced nesting. In the case of stair nesting the amount of information for the different factors is more evenly distributed. This new design leads to greater economy, because we can work with fewer observations. In this work we present the algebraic structure of the cross of balanced nested and stair nested designs, using binary operations on commutative Jordan algebras. This new cross requires fewer observations than the usual cross balanced nested designs and it is easy to carry out inference.
- Allee's effect bifurcation in generalized logistic mapsPublication . Rocha, J. Leonel; Taha, Abdel-KaddousThis paper concerns the study of the Allee effect on the dynamical behavior of a new class of generalized logistic maps. The fundamentals of the dynamics of this 4-parameter family of one-dimensional maps are presented. A complete classification of the nature and stability of its fixed points is provided. The main results relate to the Allee effect bifurcation: a new type of bifurcation introduced for this class of unimodal maps. A necessary and sufficient condition so that the Allee fixed point is a snap-back repeller is established. In addition, in the parameters space is defined an Allee's effect region, which determines the existence of an essential extinction for the generalized logistic maps. Local and global bifurcations of generalized logistic maps are investigated.
- An alternative proof on higher order derivatives of a multilinear mapPublication . Carvalho, SoniaAs a generalization of the formulas proved by Bhatia, Grover and Jain (Derivatives of tensor powers and their norms. Electron J Linear Algebra. 2013;26:604-619), in recent papers (The kth derivative of the immannant and the chi-symmetric tensor power of an operator. Electron J Linear Algebra. 2014;27:Article 18, On derivatives and norms of generalized matrix functions and respective symmetric powers. Electron J Linear Algebra. 2015;30:Article 22) Carvalho and Freitas obtained formulas for directional derivatives, of all orders, for generalized matrix functions and for every symmetric tensor power associated with a character xi of a subgroup G of the symmetric group S-m. Throughout our work, we used some well-known formulas for the derivatives of all orders of a multilinear map, since the maps that we studied are all multilinear. In this paper, we intend to present an alternative proof of these formulas, using the multilinearity argument.
- 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.
- Analytical model and measurements of the target erosion depth profile of balanced and unbalanced planar magnetron cathodesPublication . Pereira, Pedro Jorge da Silva; Escrivão, M. L.; Teixeira, M. R.; Maneira, M. J. P.; Nunes, Y.The erosion depth profile of planar targets in balanced and unbalanced magnetron cathodes with cylindrical symmetry is measured along the target radius. The magnetic fields have rotational symmetry. The horizontal and vertical components of the magnetic field B are measured at points above the cathode target with z = 2 x 10(-3) m. The experimental data reveal that the target erosion depth profile is a function of the angle. made by B with a horizontal line defined by z = 2 x 10(-3) m. To explain this dependence a simplified model of the discharge is developed. In the scope of the model, the pathway lengths of the secondary electrons in the pre-sheath region are calculated by analytical integration of the Lorentz differential equations. Weighting these lengths by using the distribution law of the mean free path of the secondary electrons, we estimate the densities of the ionizing events over the cathode and the relative flux of the sputtered atoms. The expression so deduced correlates for the first time the erosion depth profile of the target with the angle theta. The model shows reasonably good fittings to the experimental target erosion depth profiles confirming that ionization occurs mainly in the pre-sheath zone.
- Application of the Mott-Schottky model to select potentials for EIS studies on electrodes for electrochemical charge storagePublication . Adan-Mas, Alberto; Moura E Silva, Teresa; Guerlou-Demourgues, Liliane; MONTEMOR, MARIAElectrochemical Impedance Spectroscopy (EIS) is a powerful technique to understand the electrode-electrolyte interaction and to evaluate degradation, resistive behaviour and electrochemical activity of energy storage materials used in batteries, pseudocapacitors and supercapacitors among others. However, it can sometimes be misused or under-interpreted. To effectively acquire EIS results, the voltages imposed to the working electrode at which EIS spectra are obtained, shall be critically selected. This work follows a previous study on the EIS response of Nickel-Cobalt hydroxide, and highlights how the Mott-Schottky model can be used as a complementary tool to explain EIS results obtained at different potentials. The Mott-Schottky model is used to understand further the fundamental processes occurring at the electrode-electrolyte interface of nickel-cobalt hydroxide in alkali media and to explain the changes in conductivity of the material that ultimately determine the electrode electrochemical activity. The applicability of the model to assist in the potential selection for EIS studies on other important charge storage materials such as MnOx and MoOx is discussed too.
- Assessing static and dynamic response variability due to parametric uncertainty on fibre-reinforced compositesPublication . Carvalho, Alda; Silva, Tiago A. N.; Ramos Loja, M.A.Composite structures are known for their ability to be tailored according to specific operating requisites. Therefore, when modelling these types of structures or components, it is important to account for their response variability, which is mainly due to significant parametric uncertainty compared to traditional materials. The possibility of manufacturing a material according to certain needs provides greater flexibility in design but it also introduces additional sources of uncertainty. Regardless of the origin of the material and/or geometrical variabilities, they will influence the structural responses. Therefore, it is important to anticipate and quantify these uncertainties as much as possible. With the present work, we intend to assess the influence of uncertain material and geometrical parameters on the responses of composite structures. Behind this characterization, linear static and free vibration analyses are performed considering that several material properties, the thickness of each layer and the fibre orientation angles are deemed to be uncertain. In this study, multivariable linear regression models are used to model the maximum transverse deflection and fundamental frequency for a given set of plates, aiming at characterizing the contribution of each modelling parameter to the explanation of the response variability. A set of simulations and numerical results are presented and discussed.