Publications 2020

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39.  A new mathematical model for the efficiency calculation

Galindro, Aníbal and Santos, Micael and Torres, Delfim F. M. and Marta-Costa, Ana

Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications. Studies in Systems, Decision and Control

Springer Nature

During the past sixty years, a lot of effort has been made regarding the productive efficiency. Such endeavours provided an extensive bibliography on this subject, culminating in two main methods, named the Stochastic Frontier Analysis (parametric) and Data Envelopment Analysis (non-parametric). The literature states this methodology also as the benchmark approach, since the techniques compare the sample upon a chosen “more-efficient” reference. This article intends to disrupt such premise, suggesting a mathematical model that relies on the optimal input combination, provided by a differential equation system instead of an observable sample. A numerical example is given, illustrating the application of our model’s features.

ria.ua.pt | doi | Peer Reviewed

38.  Parametric identification of the dynamics of inter-sectoral balance: modelling and forecasting

Kostylenko, Olena and Rodrigues, Helena Sofia and Torres, Delfim F. M.

Recent Advances in Modeling, Analysis and Systems Control: Theoretical Aspects and Applications. Studies in Systems, Decision and Control

Springer

This work is devoted to modelling and identification of the dynamics of the inter-sectoral balance of a macroeconomic system. An approach to the problem of specification and identification of a weakly formalized dynamical system is developed. A matching procedure for parameters of a linear stationary Cauchy problem with a decomposition of its upshot trend and a periodic component, is proposed. Moreover, an approach for detection of significant harmonic waves, which are inherent to real macroeconomic dynamical systems, is developed.

ria.ua.pt | doi | Peer Reviewed

37.  An extension of the fractional Gronwall inequality

Almeida, Ricardo and Malinowska, Agnieszka B. and Odzijewicz, Tatiana

Advances in Non-Integer Order Calculus and Its Applications

Springer

In this work, we prove a generalization of the Gronwall type inequality. This relation can be used in the qualitative analysis of the solutions to fractional differential equations with the ψ-fractional derivatives.

ria.ua.pt | doi | Peer Reviewed

36.  A note on controlled invariance for behavioral nD systems

Pereira, Ricardo and Rocha, Paula

Algebraic and Symbolic Computation Methods in Dynamical Systems

Springer

In this chapter we extend the notion of invariance of nD behaviors introduced in Pereira and Rocha (European Control Conference 2013, ECC’13. ETH Zurich, Switzerland, pp. 301–305, 2013) [4], Rocha and Wood (Int. J. Appl. Math. Comput. Sci. 7(4):869–879, 1997) [7] to the controlsetting. More concretely, we introduce a notion which is the behavioral counterpart of classical controlled invariance, using the framework of partial interconnections. In such interconnections, the variables are divided into two sets: the variables to-be-controlled and the variables on which it is allowed to enforce restrictions (called control variables). In particular we focus on regular partial interconnection, i.e., interconnections in which the restrictions of the controller do not overlap with the ones already implied by the laws of the original behavior. For some particular cases, complete characterizations of controlled invariance and controller construction procedures are derived for both 1D and nD behaviors.

ria.ua.pt | doi | Peer Reviewed

35.  On SICA models for HIV transmission

Silva, Cristiana J. and Torres, Delfim F. M.

Mathematical Modelling and Analysis of Infectious Diseases. Studies in Systems, Decision and Control

Springer

We revisit the SICA (Susceptible-Infectious-Chronic-AIDS) mathematical model for transmission dynamics of the human immunodeficiency virus (HIV) with varying population size in a homogeneously mixing population. We consider SICA models given by systems of ordinary differential equations and some generalizations given by systems with fractional and stochastic differential operators. Local and global stability results are proved for deterministic, fractional, and stochastic-type SICA models. Two case studies, in Cape Verde and Morocco, are investigated.

ria.ua.pt | doi | Peer Reviewed

34.  A survey on sufficient optimality conditions for delayed optimal control problems

Lemos-Paião, Ana P. and Silva, Cristiana J. and Torres, Delfim F. M.

Mathematical Modelling and Analysis of Infectious Diseases. Studies in Systems, Decision and Control

Springer

The aim of this work is to make a survey on recent sufficient optimality conditions for optimal control problems with time delays in both state and control variables. The results are obtained by transforming delayed optimal control problems into equivalent non-delayed problems. Such approach allows to use standard theorems that ensure sufficient optimality conditions for non-delayed optimal control problems. Examples are given with the purpose to illustrate the results.

ria.ua.pt | doi | Peer Reviewed

Articles


33.  Numerical optimal control of HIV transmission in Octave/MATLAB

Campos, Carlos and Silva, Cristiana J. and Torres, Delfim F. M.

Mathematical and Computational Applications

MDPI

We provide easy and readable GNU Octave/MATLAB code for the simulation of mathematical models described by ordinary differential equations and for the solution of optimal control problems through Pontryagin’s maximum principle. For that, we consider a normalized HIV/AIDS transmission dynamics model based on the one proposed in our recent contribution (Silva, C.J.; Torres, D.F.M. A SICA compartmental model in epidemiology with application to HIV/AIDS in Cape Verde. Ecol. Complex. 2017, 30, 70–75), given by a system of four ordinary differential equations. An HIV initial value problem is solved numerically using the ode45 GNU Octave function and three standard methods implemented by us in Octave/MATLAB: Euler method and second-order and fourth-order Runge–Kutta methods. Afterwards, a control function is introduced into the normalized HIV model and an optimal control problem is formulated, where the goal is to find the optimal HIV prevention strategy that maximizes the fraction of uninfected HIV individuals with the least HIV new infections and cost associated with the control measures. The optimal control problem is characterized analytically using the Pontryagin Maximum Principle, and the extremals are computed numerically by implementing a forward-backward fourth-order Runge–Kutta method. Complete algorithms, for both uncontrolled initial value and optimal control problems, developed under the free GNU Octave software and compatible with MATLAB are provided along the article.

ria.ua.pt | doi | Peer Reviewed

32.  Regional enlarged observability of Caputo fractional differential equations

Zouiten, Hayat and Boutoulout, Ali and Torres, Delfim F. M.

Discrete and Continuous Dynamical Systems - Series S

American Institute of Mathematical Sciences (AIMS)

We consider the regional enlarged observability problem for fractional evolution differential equations involving Caputo derivatives. Using the Hilbert Uniqueness Method, we show that it is possible to rebuild the initial state between two prescribed functions only in an internal subregion of the whole domain. Finally, an example is provided to illustrate the theory.

ria.ua.pt | doi | Peer Reviewed

31.  On Hermite-Hadamard type inequalities for harmonical h-convex interval-valued functions

Dafang Zhao and Tianqing An and Guoju Ye and Torres, Delfim F. M.

Mathematical Inequalities and Applications

Ele-Math

We introduce and investigate the concept of harmonical h-convexity for interval-valued functions. Under this new concept, we prove some new Hermite-Hadamard type inequalities for the interval Riemann integral.

ria.ua.pt | doi | Peer Reviewed

30.  Traveling wave solutions of some important Wick-type fractional stochastic nonlinear partial differential equations

Hyunsoo Kim and Sakthivel, Rathinasamy and Debbouche, Amar and Torres, Delfim F. M.

Chaos, Solitons and Fractals

Elsevier

In this article, exact traveling wave solutions of a Wick-type stochastic nonlinear Schrödinger equation and of a Wick-type stochastic fractional Regularized Long Wave-Burgers (RLW-Burgers) equation have been obtained by using an improved computational method. Specifically, the Hermite transform is employed for transforming Wick-type stochastic nonlinear partial differential equations into deterministic nonlinear partial differential equations with integral and fraction order. Furthermore, the required set of stochastic solutions in the white noise space is obtained by using the inverse Hermite transform. Based on the derived solutions, the dynamics of the considered equations are performed with some particular values of the physical parameters. The results reveal that the proposed improved computational technique can be applied to solve various kinds of Wick-type stochastic fractional partial differential equations.

ria.ua.pt | doi | Peer Reviewed

29.  The stability and stabilization of infinite dimensional Caputo-time fractional differential linear systems

Zitane, Hanaa and Boutoulout, Ali and Torres, Delfim F. M.

Mathematics

MDPI

We investigate the stability and stabilization concepts for infinite dimensional time fractional differential linear systems in Hilbert spaces with Caputo derivatives. Firstly, based on a family of operators generated by strongly continuous semigroups and on a probability density function, we provide sufficient and necessary conditions for the exponential stability of the considered class of systems. Then, by assuming that the system dynamics is symmetric and uniformly elliptic and by using the properties of the Mittag-Leffler function, we provide sufficient conditions that ensure strong stability. Finally, we characterize an explicit feedback control that guarantees the strong stabilization of a controlled Caputo time fractional linear system through a decomposition approach. Some examples are presented that illustrate the effectiveness of our results.

ria.ua.pt | doi | Peer Reviewed

28.  A mathematical model for vineyard replacement with nonlinear binary control optimization

Galindro, Aníbal and Cerveira, Adelaide and Torres, Delfim F. M. and Matias, João and Marta-Costa, Ana

Discontinuity, Nonlinearity, and Complexity

L&H Scientific Publishing

Vineyard replacement is a common practice in every wine-growing farm since the grapevine production decays over time and requires a new vine to ensure the business sustainability. In this paper, we formulate a simple discrete model that captures the vineyard’s main dynamics such as production values and grape quality. Then, by applying binary nonlinear programming methods to find the vineyard replacement trigger, we seek the optimal solution concerning different governmental subsidies to the target producer.

ria.ua.pt | doi | Peer Reviewed

27.  Errata to "Modeling and optimal control of HIV/AIDS prevention through PrEP", Discrete Contin. Dyn. Syst. Ser. S 11 (2018), no. 1, 119–141

Silva, Cristiana J. and Torres, Delfim F. M.

Discrete and Continuous Dynamical Systems - Series S

American Institute of Mathematical Sciences (AIMS)

No abstract available.

ria.ua.pt | doi | Peer Reviewed

26.  Enlarged controllability and optimal control of sub-diffusion processes with Caputo fractional derivatives

Karite, Touria and Boutoulout, Ali and Torres, Delfim F. M.

Progress in Fractional Differentiation and Applications

Natural Sciences Publishing (NSP)

We investigate the exact enlarged controllability and optimal control of a fractional diffusion equation in Caputo sense. This is done through a new definition of enlarged controllability that allows us to extend available contributions. Moreover, the problem is studied using two approaches: a reverse Hilbert uniqueness method, generalizing the approach introduced by Lions in 1988, and a penalization method, which allow us to characterize the minimum energy control.

ria.ua.pt | doi | Peer Reviewed

25.  Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan

Ndaïrou, Faïçal and Area, Iván and Nieto, Juan J. and Torres, Delfim F. M.

Chaos, Solitons and Fractals

Elsevier

We propose a compartmental mathematical model for the spread of the COVID-19 disease with special focus on the transmissibility of super-spreaders individuals. We compute the basic reproduction number threshold, we study the local stability of the disease free equilibrium in terms of the basic reproduction number, and we investigate the sensitivity of the model with respect to the variation of each one of its parameters. Numerical simulations show the suitability of the proposed COVID-19 model for the outbreak that occurred in Wuhan, China.

ria.ua.pt | doi | Peer Reviewed

24.  Synchronization and self-organization in complex networks for a tuberculosis model

Silva, Cristiana J. and Cantin, Guillaume

Mathematics in Computer Science

Springer

In this work, we propose and analyze the dynamics of a complex network built with non identical instances of a tuberculosis (TB) epidemiological model, for which we prove the existence of non-negative and bounded global solutions. A two nodes network is analyzed where the nodes represent the TB epidemiological situation of the countries Angola and Portugal. We analyze the effect of different coupling and intensity of migratory movements between the two countries and explore the effect of seasonal migrations. For a random complex network setting, we show that it is possible to reach a synchronization state by increasing the coupling strength and test the influence of the topology in the dynamics of the complex network. All the results are analyzed through numerical simulations where the given algorithms are implemented with the python 3.5 language, in a Debian/GNU-Linux environment.

ria.ua.pt | doi | Peer Reviewed

23.  On leader-following consensus in multi-agent systems with discrete updates at random times

Almeida, Ricardo and Girejko, Ewa and Hristova, Snezhana and Malinowska, Agnieszka

Entropy

MDPI

This paper studies the leader-following consensus problem in continuous-time multi-agent networks with communications/updates occurring only at random times. The time between two consecutive controller updates is exponentially distributed. Some sufficient conditions are derived to design the control law that ensures the leader-following consensus is asymptotically reached (in the sense of the expected value of a stochastic process). The numerical examples are worked out to demonstrate the effectiveness of our theoretical results.

ria.ua.pt | doi | Peer Reviewed

22.  Optimal control of aquatic diseases: a case study of Yemen’s cholera outbreak

Lemos-Paião, Ana P. and Silva, Cristiana J. and Torres, Delfim F. M. and Venturino, Ezio

Journal of Optimization Theory and Applications

Springer

We propose a mathematical model for the transmission dynamics of some strains of the bacterium Vibrio cholerae, responsible for the cholera disease in humans. We prove that, when the basic reproduction number is equal to one, a transcritical bifurcation occurs for which the endemic equilibrium emanates from the disease-free point. A control function is introduced into the model, representing the distribution of chlorine water tablets for water purification. An optimal control problem is then proposed and analyzed, where the goal is to determine the fraction of susceptible individuals who should have access to chlorine water tablets in order to minimize the total number of new infections plus the total cost associated with the distribution of chlorine water tablets, over the considered period of time. Finally, we consider real data of the cholera outbreak in Yemen, from April 27, 2017 to April 15, 2018, choosing the values of the parameters of the uncontrolled model that fit the real data. Using our optimal control results, we show, numerically, that the distribution of chlorine water tablets could have stopped, in a fast way, the worst cholera outbreak that ever occurred in human history. Due to the critical situation of Yemen, we also simulate the case where only a small percentage of susceptible individuals has access to chlorine water tablets and obtain an optimal control solution that decreases, substantially, the maximum number of infective individuals affected by the outbreak.

ria.ua.pt | doi | Peer Reviewed

21.  Constructions of MDS convolutional codes using superregular matrices

Lieb, Julia and Pinto, Raquel

Journal of Algebra Combinatorics Discrete Structures and Applications

Jacodesmath Institute

Maximum distance separable convolutional codes are the codes that present best performance in error correction among all convolutional codes with certain rate and degree. In this paper, we show that taking the constant matrix coefficients of a polynomial matrix as submatrices of a superregular matrix, we obtain a column reduced generator matrix of an MDS convolutional code with a certain rate and a certain degree. We then present two novel constructions that fulfill these conditions by considering two types of superregular matrices.

ria.ua.pt | Peer Reviewed

20.  Functional differential equations involving the ψ-Caputo fractional derivative

Almeida, Ricardo

Fractal and Fractional

MDPI

This paper is devoted to the study of existence and uniqueness of solutions for fractional functional differential equations, whose derivative operator depends on an arbitrary function. The introduction of such function allows generalization of some known results, and others can be also obtained.

ria.ua.pt | doi | Peer Reviewed

19.  Dynamical analysis of a fractional SIR model with treatment and quarantine

Almeida, Ricardo

Chaotic Modeling and Simulation

We propose a fractional SIR model with treatment and quarantine policies, whose dynamics is described by the Caputo fractional derivative. Local stability of the equilibrium points is studied, and the threshold value R0 is found. Finally, some numerical simulations are presented for different values of the parameters.

ria.ua.pt | Peer Reviewed

18.  A stochastic fractional calculus with applications to variational principles

Zine, Houssine and Torres, Delfim F. M.

Fractal and Fractional

MDPI

We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional Euler-Lagrange equation is obtained, extending those available in the literature for the classical, fractional, and stochastic calculus of variations. To illustrate our main theoretical result, we discuss two examples: one derived from quantum mechanics, the second validated by an adequate numerical simulation.

ria.ua.pt | doi | Peer Reviewed

17.  Lyapunov functions for fractional-order systems in biology: methods and applications

Boukhouima, Adnane and Hattaf, Khalid and Lotfi, El Mehdi and Mahrouf, Marouane and Torres, Delfim F. M. and Yousfi, Noura

Chaos, Solitons & Fractals

Elsevier

We prove new estimates of the Caputo derivative of order α ∈ (0, 1] for some specific functions. The estimations are shown useful to construct Lyapunov functions for systems of fractional differential equations in biology, based on those known for ordinary differential equations, and therefore useful to determine the global stability of the equilibrium points for fractional systems. To illustrate the usefulness of our theoretical results, a fractional HIV population model and a fractional cellular model are studied. More precisely, we construct suitable Lyapunov functionals to demonstrate the global stability of the free and endemic equilibriums, for both fractional models, and we also perform some numerical simulations that confirm our choices.

ria.ua.pt | doi | Peer Reviewed

16.  Corrigendum to "Mathematical Modeling of COVID-19 Transmission Dynamics with a Case Study of Wuhan" [Chaos Solitons Fractals 135 (2020), 109846]

Ndaïrou, Faïçal and Area, Iván and Bader, Georg and Nieto, Juan J. and Torres, Delfim F. M.

Chaos, Solitons and Fractals

Elsevier

We correct some numerical results of [Chaos Solitons Fractals 135 (2020), 109846], by providing the correct numbers and plots. The conclusions of the paper remain, however, the same. In particular, the numerical simulations show the suitability of the proposed COVID-19 model for the outbreak that occurred in Wuhan, China. This time all our computer codes are provided, in order to make all computations reproducible. The authors would like to apologize for any inconvenience caused.

ria.ua.pt | doi | Peer Reviewed

15.  Fractional variational principle of Herglotz for a new class of problems with dependence on the boundaries and a real parameter

Almeida, Ricardo and Martins, Natália

Journal of Mathematical Physics

American Institute of Physics

The fractional variational problem of Herglotz type for the case where the Lagrangian depends on generalized fractional derivatives, the free endpoints conditions, and a real parameter is studied. This type of problem generalizes several problems recently studied in the literature. Moreover, it allows us to unify conservative and non-conservative dynamical processes in the same model. The dependence of the Lagrangian with respect to the boundaries and a free parameter is effective and transforms the standard Herglotz’s variational problem into a problem of a different nature.

ria.ua.pt | doi | Peer Reviewed

14.  Application of Bernoulli polynomials for solving variable-order fractional optimal control-affine problems

Nemati, Somayeh and Torres, Delfim F. M.

Axioms

MDPI

We propose two efficient numerical approaches for solving variable-order fractional optimal control-affine problems. The variable-order fractional derivative is considered in the Caputo sense, which together with the Riemann--Liouville integral operator is used in our new techniques. An accurate operational matrix of variable-order fractional integration for Bernoulli polynomials is introduced. Our methods proceed as follows. First, a specific approximation of the differentiation order of the state function is considered, in terms of Bernoulli polynomials. Such approximation, together with the initial conditions, help us to obtain some approximations for the other existing functions in the dynamical control-affine system. Using these approximations, and the Gauss--Legendre integration formula, the problem is reduced to a system of nonlinear algebraic equations. Some error bounds are then given for the approximate optimal state and control functions, which allow us to obtain an error bound for the approximate value of the performance index. We end by solving some test problems, which demonstrate the high accuracy of our results.

ria.ua.pt | doi | Peer Reviewed

13.  Distributed-order non-local optimal control

Ndaïrou, Faïçal and Torres, Delfim F. M.

Axioms

MDPI

Distributed-order fractional non-local operators were introduced and studied by Caputo at the end of the 20th century. They generalize fractional order derivatives/integrals in the sense that such operators are defined by a weighted integral of different orders of differentiation over a certain range. The subject of distributed-order non-local derivatives is currently under strong development due to its applications in modeling some complex real world phenomena. Fractional optimal control theory deals with the optimization of a performance index functional, subject to a fractional control system. One of the most important results in classical and fractional optimal control is the Pontryagin Maximum Principle, which gives a necessary optimality condition that every solution to the optimization problem must verify. In our work, we extend the fractional optimal control theory by considering dynamical system constraints depending on distributed-order fractional derivatives. Precisely, we prove a weak version of Pontryagin’s maximum principle and a sufficient optimality condition under appropriate convexity assumptions.

ria.ua.pt | doi | Peer Reviewed

12.  Mathematical modeling of Japanese encephalitis under aquatic environmental effects

Ndaïrou, Faïçal and Area, Iván and Torres, Delfim F. M.

Mathematics

MDPI

We propose a mathematical model for the spread of Japanese encephalitis with emphasis on the environmental effects on the aquatic phase of mosquitoes. The model is shown to be biologically well-posed and to have a biologically and ecologically meaningful disease-free equilibrium point. Local stability is analyzed in terms of the basic reproduction number and numerical simulations presented and discussed.

ria.ua.pt | doi | Peer Reviewed

11.  A stochastic time-delayed model for the effectiveness of Moroccan COVID-19 deconfinement strategy

Zine, Houssine and Boukhouima, Adnane and Lotfi, El Mehdi and Mahrouf, Marouane and Torres, Delfim F. M. and Yousfi, Noura

Mathematical Modelling of Natural Phenomena

EDP Sciences

Coronavirus disease 2019 (COVID-19) poses a great threat to public health and the economy worldwide. Currently, COVID-19 evolves in many countries to a second stage, characterized by the need for the liberation of the economy and relaxation of the human psychological effects. To this end, numerous countries decided to implement adequate deconfinement strategies. After the first prolongation of the established confinement, Morocco moves to the deconfinement stage on May 20, 2020. The relevant question concerns the impact on the COVID-19 propagation by considering an additional degree of realism related to stochastic noises due to the effectiveness level of the adapted measures. In this paper, we propose a delayed stochastic mathematical model to predict the epidemiological trend of COVID-19 in Morocco after the deconfinement. To ensure the well-posedness of the model, we prove the existence and uniqueness of a positive solution. Based on the large number theorem for martingales, we discuss the extinction of the disease under an appropriate threshold parameter. Moreover, numerical simulations are performed in order to test the efficiency of the deconfinement strategies chosen by the Moroccan authorities to help the policy makers and public health administration to make suitable decisions in the near future.

ria.ua.pt | doi | Peer Reviewed

10.  A new compartmental epidemiological model for COVID-19 with a case study of Portugal

Lemos-Paião, Ana P. and Silva, Cristiana J. and Torres, Delfim F. M.

Ecological Complexity

Elsevier

We propose a compartmental mathematical model for the spread of the COVID-19 disease, showing its usefulness with respect to the pandemic in Portugal, from the first recorded case in the country till the end of the three states of emergency. New results include the compartmental model, described by a system of seven ordinary differential equations; proof of positivity and boundedness of solutions; investigation of equilibrium points and their stability analysis; computation of the basic reproduction number; and numerical simulations with official real data from the Portuguese health authorities. Besides completely new, the proposed model allows to describe quite well the spread of COVID-19 in Portugal, fitting simultaneously not only the number of active infected individuals but also the number of hospitalized individuals, respectively with a $L^2$ error of $9.2152e-04$ and $1.6136e-04$ with respect to the initial population. Such results are very important, from a practical point of view, and far from trivial from a mathematical perspective. Moreover, the obtained value for the basic reproduction number is in agreement with the one given by the Portuguese authorities at the end of the emergency states.

ria.ua.pt | doi | Peer Reviewed

9.  An adaptive bolus calculator to minimize the impact of inaccurate insulin to carbohydrate ratio

Miranda, Francisco and Abreu, Carlos and Felgueiras, Paula

AIP Conference Proceedings

AIP Publishing

Patients with type 1 diabetes mellitus use intensive insulin therapy to suppress their insulin needs and avoid the adverse consequences of chronic hyperglycemia. Intensive insulin therapy consists of a combination of basal insulin and bolus insulin. While the basal insulin dose is periodically adjusted in collaboration with the healthcare team, patients have to estimate the bolus insulin dose by themselves, before each meal. To accurately estimate the bolus insulin dose, patients must know the carbohydrates content of each meal and their insulin to carbohydrate ratio. The insulin to carbohydrate ratio is initially calculated by experienced diabetologists using high-quality data. However, regarding the glucose complex metabolism, it varies over the day due to several factors. Consequently, daily, patients use approximate values to estimate their bolus insulin. Thus, depending on the error of the insulin to carbohydrate ratio estimates, the patient could experience hypo or hyperglycemic events. Therefore, to avoid the consequences of inaccurate bolus insulin and to improve the patient's glycemic control, this work presents an adaptive insulin bolus calculator that uses the patient's glycemic data to dynamically adjust the mealtime bolus and compensate for the adverse effects of inaccurate insulin to carbohydrate ratio estimates.

ria.ua.pt | doi | Peer Reviewed

8.  Assessing the impact of inaccurate insulin-to-carbohydrate ratio on the patient's glycemic targets and lifestyle management

Miranda, Francisco and Abreu, Carlos and Felgueiras, Paula

AIP Conference Proceedings

AIP Publishing

To mitigate the adverse consequences of chronic hyperglycemia, patients with type 1 diabetes mellitus must provide their bodies with insulin to control their blood glucose. In most cases, insulin therapy consists of a combination of basal insulin and bolus insulin, the so-called basal-bolus insulin therapy. To determine the bolus insulin, patients must know not only the carbohydrate content of each meal but also the values of the insulin-to-carbohydrate ratio and the insulin sensitivity factor. Although important, the blood glucose complex dynamics make determining these parameters a difficult and error-prone task, usually performed by experienced diabetologists using high-quality data. Moreover, the insulin-to-carbohydrate ratio and the insulin sensitivity factor vary over the day due to several factors. Thus, daily, patients use approximate values to determine their prandial bolus. In this paper, we propose an analytic method to find the safe maximum interval for the error in the estimates of the insulin-to-carbohydrate ratio and, therefore, avoid dysglycemia. Our study suggests that slimmer patients with smaller insulin-to-carbohydrate ratios need to be more careful when estimating it. Another significant finding of our work is that in such cases, having small meals reduces the adverse effect of inaccurate insulin-to-carbohydrate ratio estimates in the postprandial blood glucose.

ria.ua.pt | doi | Peer Reviewed

7.  Theoretical simulation of different 3D separator geometries for lithium-ion batteries

Miranda, D. and Gonçalves, R. and Miranda, F. and Almeida, A. M. and Costa, C. M. and Lanceros-Méndez, S.

AIP Conference Proceedings

AIP Publishing

The battery separator is an essential component of batteries and affects their cycling performance. In this work, the effect of different 3D geometries of the battery separator on battery performance was studied keeping the same volume. It was observed that the different geometries affect the cycling performance, the best geometry being the perforated one that cycled up to 90 C. The cycling performance is affected by parameters such as the separator thickness and the electrolyte volume. Through the control of the battery separator geometry it is possible to obtain high performance lithium-ion batteries.

ria.ua.pt | doi | Peer Reviewed

6.  Preface of the “5th Symposium on Modelling and Simulation in Computer Sciences and Engineering”

Miranda, Francisco and Abreu, Carlos and Miranda, Daniel

AIP Conference Proceedings

AIP Publishing

The 5th Symposium on Modelling and Simulation in Computer Sciences and Engineering was held in the 17th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2019), Rhodes, Greece, 23-28 September 2019.

ria.ua.pt | doi | Peer Reviewed

5.  Cone geometry optimization and thermal behavior for lithium-ion battery separators

Miranda, D. and Gonçalves, R. and Miranda, F. and Vilhena, E. and Lanceros-Méndez, S. and Costa, C. M.

AIP Conference Proceedings

AIP Publishing

A 3D cone separator geometry for lithium-ion batteries has been optimized taking into account the increase of radius size of one side. Theoretical simulations have been carried out for evaluating the influence of radius size in the cone structure at different discharge rates (1 C and 60 C) in which it was also determined the produced ohmic heat. The value of the discharge capacity in the cone structure depends on the increases of the radius, which is correlated with the electrolyte volume and interface between free electrolyte/cathode. The optimum balance of these parameters is essential for obtaining higher battery performance through this geometry that can be used in the next generation of lithium-ion batteries.

ria.ua.pt | doi | Peer Reviewed

4.  On the existence of optimal consensus control for the fractional Cucker–Smale model

Almeida, R. and Kamocki, R. and Malinowska, A. B. and Odzijewicz, T.

Archives of Control Sciences

PAN

This paper addresses the nonlinear Cucker–Smale optimal control problem under the interplay of memory effect. The aforementioned effect is included by employing the Caputo fractional derivative in the equation representing the velocity of agents. Sufficient conditions for the existence of solutions to the considered problem are proved and the analysis of some particular problems is illustrated by two numerical examples.

ria.ua.pt | doi | Peer Reviewed

3.  A behavioral approach to estimation in nD systems

Pereira, Ricardo and Rocha, Paula

IFAC-PapersOnLine

Elsevier; International Federation of Automatic Control (IFAC)

In this paper we study the problem of estimation for multidimensional systems within the context of the behavioral approach. We consider the case where there are no disturbances as well as the case where the system dynamics is perturbed, and provide necessary conditions for the solvability of the corresponding estimation problems together with the construction of a solution, if it exists. Such solution is an estimator that is asymptotic, in the sense that the error trajectories are stable with respect to a pre-specified nD stability cone.

ria.ua.pt | doi | Peer Reviewed

Proceedings


2.  On the use of neural networks for stock price forecasting

Sousa, Virgínia and Alonso, Hugo

Economic and Social Development: 62nd International Scientific Conference on Economic and Social Development: book of proceedings

Varazdin Development and Entrepreneurship Agency; University North

Having the ability to predict the price of a particular stock share is undoubtedly a major challenge, because of the complexity and implied volatility of the financial markets. This is a topic of great interest to researchers and market players, as the effectiveness of the forecast might translate into huge monetary gains. This work aims to demonstrate the use of neural networks for stock price forecasting. Two financial titles are considered: Microsoft and Apple. The initial choice of the predictor variables comprises the most used and referenced in the scientific papers published on this subject. This work demonstrates the importance of a careful selection of some of those variables for a good neural network performance.

ria.ua.pt | Peer Reviewed

1.  Situational pricing: the role of wine consumption occasion on price decision

Candeias, Teresa and Alonso, Hugo

Economic and Social Development: 62nd International Scientific Conference on Economic and Social Development: book of proceedings

Varazdin Development and Entrepreneurship Agency; University North

Wine companies are usually operating in larger and diverse markets and consumers show different needs. Given resource constraints, companies must segment the market, because they cannot cover the entire market or, if they do, they need to adopt and implement an appropriate marketing strategy. Market segmentation enables to treat consumers differently through a marketing strategy geared to this purpose. There are several segmentation criteria and one of them is the wine consumption occasion. Here, like other authors do, we consider the following five situations where the consumer pays for a bottle of wine: to drink at home, to drink at home with friends, to drink at a restaurant, to give as a gift and in businesses. We asked to 133 consumers, randomly selected, how much they were willing to pay in each situation: < 1 Euro; 1 – 2 Euros; 2 – 5 Euros; 5 – 10 Euros; 10 – 20 Euros; > 20 Euros. We concluded that the price decision depends on the wine consumption occasion (Friedman test, p-value=0,000). This is in accordance with the literature. Furthermore, we found something that, to our knowledge, is new: at a 5% level of significance, there is no difference between the situations “to drink at home” and “to drink at home with friends” and also between “to drink at a restaurant”, “to give as a gift” and “in businesses”; the difference lies between the former two situations and the latter three. This means that, for market segmentation, we can consider two instead of five wine consumption occasions. We further investigate how this conclusion depends on consumer gender.

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