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ABSTRACT The calculation of the Coulomb Potential corresponding to the product of two Exponential Type Functions, inherently has numerical challenges that must be resolved. In order to address these problems, in this paper it is presented a new partition of the Coulomb Potential. The proposed partition involves two terms. One of the terms is a one-dimensional integral, which allows geometrical and statistical interpretations. The other term is proportional to a Modified Bessel Function and it is obtained from a two-step procedure. As a first step, a Non-Rational Function is used for approximating one of the two integrals involved. Then, the remaining improper integral can be identified with an integral representation of an appropriate Modified Bessel Function. The existence of such a Non-Rational Approximant is proved and its numerical performance is shown through some examplesResumo em Inglês:
ABSTRACT In this work we analyze the approximation error in Sobolev norms for quasi-interpolation operators in spline spaces. We establish in a general way the hypotheses on a quasi-interpolant to achieve the optimal order of approximation. Finally, we propose simple but general constructions of such operators that satisfy the established hypotheses and illustrate their performance through some numerical tests.Resumo em Inglês:
ABSTRACT The d-minimal path (d-MP) problem is to find all the system state vectors (SSV) under which d units of data can be transmitted from a source node to a destination node in a stochastic-flow network (SFN). This problem has been very attractive in the last decades as one can compute the exact amount of the network’s reliability through the d-MPs. Although several algorithms have been proposed in the literature to address the problem, the research continues because it is NP-hard. Since the number of d-MPs grows exponentially with the size of the network, the available algorithms in the literature are not so practical. Hence, we employ the vectorization techniques for proposing an improved algorithm to address the problem. We conduct many experimental results on the known benchmarks and two hundred randomly generated SFNs in the sense of performance profile introduced by Dolan and Moré. The experimental results show the vectorization algorithm to be considerably more efficient than the non-vectorization ones.Resumo em Inglês:
ABSTRACT Within metal constructions there are structures made up of parallel members called legs, connected to each other by diagonals. Some of these structures, with a triangular cross section, turn out to be the guyed masts used in the communications industry, but also columns and beams used in metal structures. In the present work, the equations that allow obtaining the equations of the elastic of a spatial lattice of triangular cross section are developed, in which the legs are joined together by zig-zag diagonals. To do this, we start from an energy proposal in which the differential equations of equilibrium and the boundary conditions of the proposed problem are determined. Finally, examples are presented where results are obtained with the equations developed, and they are compared with the results obtained from the application of the expressions given in CIRSOC 303 Recommendation (1996) and from finite element models.Resumo em Inglês:
ABSTRACT In this work, error estimates are presented for the case in which the regularized solution is obtained by minimizing doubly-generalized Tikhonov-Phillips functionals. The first result is based mainly on an assumption given by a source condition. It is proved that it is possible to replace this assumption by a variational inequality, obtaining analogous result of the error estimate. Finally, relationships are established between the optimality condition associated with the problem, the source condition and the variational inequality. On the other hand, it is known that, in certain cases, the use of two or more penalizing terms is useful. For this reason, generalizations of the results of error estimates are presented for cases in which the regularized solution is a minimizer of doubly-generalized Tikhonov-Phillips functionals with multiple penalizers.Resumo em Inglês:
ABSTRACT The auditory brainstem response (ABR) by evoked potentials is a widespread auditory pathway assessment technique. This is largely applied due to its cost-effectiveness, practicality and ease of use. In contrast, it requires a trained professional to carry out the analysis of the results. This motivates several research efforts to increase the independence of the diagnostician. To this end, the present work shows the ability of three signal classification tools to differentiate ABR studies of normal hearing subjects from those who may have some pathology. As a starting point, the PhysioNet short term auditory evoked potentials databases are used to calculate the features later applied to construct the dataset. The features used are diverse classes of permutation entropy, fractal dimension, the Lyapunov exponent and the zero crossing rate. To ensure more accurate results, a Montecarlo simulation of one thousand trials is employed to train the classifiers and test the results. The goodness of the classification is performed upon the basis of the computation of quality parameters, such as the area under the receiver operating characteristic curve (ROC), the F1 score coefficient and the accuracy. In all the cases the methodology proposed gives high performance results that encourage the line of research of the present work.Resumo em Inglês:
ABSTRACT Due to global warming, wildfires became more severe and frequent than in the past, and more complex mathematics is needed to provide the model of propagation and predict the behavior of the fire. In this work, for a wildfire spreading in some flat land of zero slope, by using Randers metric the equations of wavefronts and wave rays are provided which lead to presenting a more precise and reliable model of propagation. By considering some hypothetical fire in Boa Nova National Park as an example, a simulation is implemented.Resumo em Inglês:
ABSTRACT This paper presents a graphical interface called EPIGUI, which allows the study of the dynamics of an infectious disease spread using compartmental models in combination with complex networks. This interface aims at considering stochastic factors that govern the evolution of an infection in a network. Moreover, it provides simple tools to create networks of agents and to define the epidemiological parameters of outbreaks. There are six common infectious disease models (SI, SIS, SIR, SIRS, SEIR, and SEIRS) or a user can provide another model, combining compartments. Moreover, in the simulations the user can either include a synthetic network generated according to a network model (random, small-world, scalefree, modular, or hierarchical) or a real network. This approach can help understand the paths followed by outbreaks in a given community and design new strategies to prevent and to control them.Resumo em Inglês:
ABSTRACT In this work we introduce a methodology to determine an optimal vaccination strategy for the COVID-19 disease with limited vaccination capacity, considering the delays between vaccine doses in order to minimize the number of deaths. We start proposing a compartmental model in order to study the evolution of the pandemic before the existence of a vaccine, in the city of Tandil, province of Buenos Aires, Argentina. We calibrate the parameters involved according to official data. Based on that model, we design an age-structured optimal control problem to determine the best way of administrate the available vaccines, taking into account their characteristics and the vaccination capacity. Finally, we compare optimal solutions with other feasible strategies, considering or not strict isolation measures.Resumo em Inglês:
ABSTRACT Leishmaniasis is a parasite disease transmitted by the bites of sandflies. There have been found more than 70 animal species that are natural reservoir hosts of Leishmania. Among the reservoirs, dogs are the most important ones due to their proximity to the human habitat. In this work, we formulate a model to assess the impact of vaccination, insecticide-impregnated collars, and treatment on the control of canine leishmaniasis. To this end, we calculated the Basic Reproduction Number of the disease and carried out a sensitivity analysis of this parameter concerning the epidemiological and demographic parameters. The numerical simulations show the correlation between the disease prevalence and the strategies effectiveness. Control of infection on dogs can be obtained by protecting around 35 percent of dogs with vaccination and insecticide-impregnated collar.Resumo em Inglês:
ABSTRACT Over the past few years, there has been a steady increase in the use of aircraft vehicles, in particular unmanned aerial vehicles (UAV). UAV navigation is generally controlled by a human pilot. But the challenge for the scientific community is to carry out autonomous navigation. Some solutions have been proposed for the UAV autonomous navigation. Studies indicate as a solution to use data fusion and/or image processing navigation. Kalman Filter (KF) can be employed as a data fuser, but the KF has disadvantages. An alternative to the KF is based on artificial intelligence. Here, the KF is replaced by a self-configured neural network. This work investigates a way to select data for training the neural fuser, based on cross-validation techniques. The results are compared to the data fusion done by a KF.Resumo em Inglês:
ABSTRACT The characterization of inverses of symmetric tridiagonal and block tridiagonal matrices and the development of algorithms for finding the inverse of any general non-singular tridiagonal matrix are subjects that have been studied by many authors. The results of these research usually depend on the existence of the LU factorization of a non-sigular matrix A, such that A = LU . Besides, the conditions that ensure the nonsingularity of A and its LU factorization are not promptly obtained. Then, we are going to present in this work two extremely simple sufficient conditions for existence of the LU factorization of a Toeplitz symmetric tridiagonal matrix A. We take into consideration the roots of the modified Chebyshev polynomial, and we also present an analysis based on the parameters of the Crout’s method.